In this article, we secure couple of exciting common fixed point theorems via simulation function... more In this article, we secure couple of exciting common fixed point theorems via simulation functions in Branciari metric spaces context. These results improve, complement and generalize the rescent fi xed point theorems of Aydi et al. [Results Math. 71 (2017), no. 1-2, 73-92] and others. Our fi ndings are aptly endorsed by some interesting non-trivial examples which also illustrate the usefulness of these generalizations. Finally, we discuss an application of our conceived results in certain integral equations.
This paper is aimed at proving some common fixed point theorems for mappings involving generalize... more This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μ τ = ∫ 0 τ Γ τ , v , μ v d v and ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all μ ∈ U , v ∈ 0 , η , and 0 < η ∈ ℝ , where U = C 0 , η , ℝ is the space of all ℝ -valued continuous functions on the interval 0 , η and Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .
This paper aims at proving some unique fixed-point results for different contractive-type self-ma... more This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.
In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix functio... more In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function.
Recently, fractional calculus has been the center of attraction for researchers in mathematical s... more Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and mi...
In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem... more In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.
The principal motivation of this paper is to establish a new integral equality related to k-Riema... more The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.
The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominat... more The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V-contractions in modular-like metric spaces. Some theorems using a partial order are discussed and also some useful results to graphic contractions for fuzzy-graph dominated mappings are developed. To explain the validity of our results, 2D and 3D graphs have been constructed. Also, applications are provided to show the novelty of our obtained results and their usage in engineering and computer science.
In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orth... more In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is being presented.
In this article, we are generalizing the concept of control fuzzy metric spaces by introducing or... more In this article, we are generalizing the concept of control fuzzy metric spaces by introducing orthogonal control fuzzy metric spaces. We prove some fixed point results in this setting. We provide nontrivial examples to show the validity of our main results and the introduced concepts. An application to fuzzy integral equations is also included. Our results generalize and improve several developments from the existing literature.
Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contrac... more Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.
We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolati... more We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.
In this paper, we aim to introduce six new quadruple hypergeometric functions. Then, we investiga... more In this paper, we aim to introduce six new quadruple hypergeometric functions. Then, we investigate certain formulas and representations for these functions such as symbolic formulas, differential formulas, and integral representations.
In this paper, we define the notation of admissible hybrid Z -contractions in the setting of exte... more In this paper, we define the notation of admissible hybrid Z -contractions in the setting of extended b -metric spaces, which unifies and generalizes previously existing results in literature. Furthermore, as an application, we discuss Ulam-Hyers stability and well-posedness of a fixed point problem.
The aim of our study is to establish, for convex functions on an interval, a midpoint version of ... more The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.
In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the fallin... more In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy k -ideals and falling fuzzy k -ideals in hemirings. In particular, we shall establish different characterizations of k -hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy k -ideals.
Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In ... more Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In this manuscript, our goal is to initiate a new quadruple hypergeometric function denoted by X 84 4 , and then, we ensure the existence of solutions of systems of partial differential equations for this function. We also establish some integral representations involving the quadruple hypergeometric function X 84 4 .
The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric... more The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric spaces and discuss some related fixed point results to ensure the existence and uniqueness of a fixed point. A nontrivial example is imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the provided results, an application is presented to solve the first kind of a Fredholm-type integral equation.
We initiate the concept of $C^{*}$-algebra-valued $G_{b}$-metric spaces. We study some basic prop... more We initiate the concept of $C^{*}$-algebra-valued $G_{b}$-metric spaces. We study some basic properties of such spaces and then prove some fixed point theorems for Banach and Kannan types via $\mathit{C_{*}}$-class functions. Also, some nontrivial examples are presented to ensure the effectiveness and applicability of the obtained results.
This paper involves extended b − metric versions of a fractional differential equation, a system ... more This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.
In this article, we secure couple of exciting common fixed point theorems via simulation function... more In this article, we secure couple of exciting common fixed point theorems via simulation functions in Branciari metric spaces context. These results improve, complement and generalize the rescent fi xed point theorems of Aydi et al. [Results Math. 71 (2017), no. 1-2, 73-92] and others. Our fi ndings are aptly endorsed by some interesting non-trivial examples which also illustrate the usefulness of these generalizations. Finally, we discuss an application of our conceived results in certain integral equations.
This paper is aimed at proving some common fixed point theorems for mappings involving generalize... more This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μ τ = ∫ 0 τ Γ τ , v , μ v d v and ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all μ ∈ U , v ∈ 0 , η , and 0 < η ∈ ℝ , where U = C 0 , η , ℝ is the space of all ℝ -valued continuous functions on the interval 0 , η and Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .
This paper aims at proving some unique fixed-point results for different contractive-type self-ma... more This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.
In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix functio... more In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function.
Recently, fractional calculus has been the center of attraction for researchers in mathematical s... more Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and mi...
In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem... more In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.
The principal motivation of this paper is to establish a new integral equality related to k-Riema... more The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.
The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominat... more The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V-contractions in modular-like metric spaces. Some theorems using a partial order are discussed and also some useful results to graphic contractions for fuzzy-graph dominated mappings are developed. To explain the validity of our results, 2D and 3D graphs have been constructed. Also, applications are provided to show the novelty of our obtained results and their usage in engineering and computer science.
In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orth... more In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is being presented.
In this article, we are generalizing the concept of control fuzzy metric spaces by introducing or... more In this article, we are generalizing the concept of control fuzzy metric spaces by introducing orthogonal control fuzzy metric spaces. We prove some fixed point results in this setting. We provide nontrivial examples to show the validity of our main results and the introduced concepts. An application to fuzzy integral equations is also included. Our results generalize and improve several developments from the existing literature.
Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contrac... more Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.
We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolati... more We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.
In this paper, we aim to introduce six new quadruple hypergeometric functions. Then, we investiga... more In this paper, we aim to introduce six new quadruple hypergeometric functions. Then, we investigate certain formulas and representations for these functions such as symbolic formulas, differential formulas, and integral representations.
In this paper, we define the notation of admissible hybrid Z -contractions in the setting of exte... more In this paper, we define the notation of admissible hybrid Z -contractions in the setting of extended b -metric spaces, which unifies and generalizes previously existing results in literature. Furthermore, as an application, we discuss Ulam-Hyers stability and well-posedness of a fixed point problem.
The aim of our study is to establish, for convex functions on an interval, a midpoint version of ... more The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.
In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the fallin... more In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy k -ideals and falling fuzzy k -ideals in hemirings. In particular, we shall establish different characterizations of k -hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy k -ideals.
Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In ... more Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In this manuscript, our goal is to initiate a new quadruple hypergeometric function denoted by X 84 4 , and then, we ensure the existence of solutions of systems of partial differential equations for this function. We also establish some integral representations involving the quadruple hypergeometric function X 84 4 .
The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric... more The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric spaces and discuss some related fixed point results to ensure the existence and uniqueness of a fixed point. A nontrivial example is imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the provided results, an application is presented to solve the first kind of a Fredholm-type integral equation.
We initiate the concept of $C^{*}$-algebra-valued $G_{b}$-metric spaces. We study some basic prop... more We initiate the concept of $C^{*}$-algebra-valued $G_{b}$-metric spaces. We study some basic properties of such spaces and then prove some fixed point theorems for Banach and Kannan types via $\mathit{C_{*}}$-class functions. Also, some nontrivial examples are presented to ensure the effectiveness and applicability of the obtained results.
This paper involves extended b − metric versions of a fractional differential equation, a system ... more This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.
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