Papers by Basel M. Hardan
JP Journal of Fixed Point Theory and Applications
We modify the Hardy-Rogers' theorem and establish the same in an uncomplicated way. We pr... more We modify the Hardy-Rogers' theorem and establish the same in an uncomplicated way. We provide an application in support of our result.
In this paper, some necessary and sufficient conditions for an 𝑛– normed spaces to be an 𝑛–inner ... more In this paper, some necessary and sufficient conditions for an 𝑛– normed spaces to be an 𝑛–inner product spaces are given.
Advances in the Theory of Nonlinear Analysis and its Application, 2020
In this research paper, we introduce a generalization of Hardy-Rogers type contraction in a metri... more In this research paper, we introduce a generalization of Hardy-Rogers type contraction in a metric like space. Moreover, we apply this technique to investigate the existence and uniqueness of solutions for the classical boundary value problems and generalized fractional boundary value problems through deducing the main properties of the related Green functions. The main result of this paper is to establish the modified conditions of Hardy-Roger's fixed point theorem and introduce some advanced applications.
International Journal of Apllied Mathematics, 2020
In this paper, we investigate the existence and uniqueness of positive solutions of boundary valu... more In this paper, we investigate the existence and uniqueness of positive solutions of boundary value problems (BVPs) for fractional differential equations (FDEs) with boundary conditions (BCs) involving the Riemann-Liouville (RL) fractional derivative of the form: −D σ 0+ x(t) = f (t, x(t)), 0 < t < 1, x(0) = x ′ (0) = ... = x (n−2) (0) = 0, x(1) = ϑ 1 0 x(s)ds, 0 < ϑ < σ, where 2 ≤ n − 1 < σ ≤ n and σ ∈ R. The technique employed is coupled lower and upper solutions with fixed point theory on cone. An example is presented to justify our results.
Journal of Inequalities and Applications, 2014
The main purpose of this paper is to study the coincidence point and common fixed point theorems ... more The main purpose of this paper is to study the coincidence point and common fixed point theorems in the product spaces of mixed-monotonically complete quasi-ordered metric spaces based on some new types of contractive inequalities. In order to investigate the existence and chain-uniqueness of solutions for the systems of integral equations and ordinary differential equations, we shall also study the fixed point theorems for the functions having mixed monotone property or comparable property in the product space of quasi-ordered metric space. MSC: 47H10; 54H25
In this paper, a version modi ed of contraction Hardy-Rogers type in a metric space and is proved... more In this paper, a version modi ed of contraction Hardy-Rogers type in a metric space and is proved. Moreover, we apply this modi ed version to investigate the existence of unique solution of boundary value problems for the di erential equations and generalized fractional di erential equations through help of the properties of Green function. We also provide an example in support of acquired results. These results extend various comparable results from literature.
WSEAS TRANSACTIONS ON MATHEMATICS
The common fixed point for self-contractive mappings in cone 2-metric spaces over Banach algebra ... more The common fixed point for self-contractive mappings in cone 2-metric spaces over Banach algebra is established in this study. The acquired results enhance and generalise the corresponding conclusions from the literature. A numerical example and a counterexample were then provided at the end.
Journal of Drug Designing and Bioinformatics
In this paper, Cauchy-Schwarz inequality on n-inner product spaces is reproved, and notions of or... more In this paper, Cauchy-Schwarz inequality on n-inner product spaces is reproved, and notions of orthogonality on n-normed spaces are introduced. This is the first approach to orthogonality types in such spaces.
Journal of Mathematics
In this article, the existence and uniqueness of a fixed point were investigated using the concep... more In this article, the existence and uniqueness of a fixed point were investigated using the concept of σ , γ -contractive in the context of Hausdorff metric space. A well-known Caristi type is primarily generalized by the new results. The result is improved by building up an example.
Advances in Mathematical Physics
The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity
In this paper, we gave generalizations some fixed point theorems of Reich, Kannan, Chatterjee, an... more In this paper, we gave generalizations some fixed point theorems of Reich, Kannan, Chatterjee, and Roades mappings satisfying Hardy-Rogers type of contractive condition on cone 2-metric spaces over Banach algebra. The obtained results will be to improve and generalize the corresponding conclusions in the literature. In the end, an example to justify our obtained results.
Advances in Mathematical Physics
In this paper, we give a concept of η , γ f , g -contraction in the setting of expanded b –metric... more In this paper, we give a concept of η , γ f , g -contraction in the setting of expanded b –metric spaces and discuss the existence and uniqueness of a common fixed point. Introduced results generalize well-known fixed point theorems on contraction conditions and in the given spaces.
Bulletin of Pure & Applied Sciences- Mathematics and Statistics
This paper mainly focuses on the recent advances in the fixed point theory. Some discussions are ... more This paper mainly focuses on the recent advances in the fixed point theory. Some discussions are presented on the relation of fixed point theorems to applications, and areas are delineated in the future research directions as well.
Advances in Mathematical Physics
In this paper, we introduce new coincidence fixed point theorems for generalized ϕ , ψ -contracti... more In this paper, we introduce new coincidence fixed point theorems for generalized ϕ , ψ -contractive mappings fulfilling kind of an admissibility provision in a Hausdorff b -rectangular metric space with the support of C-functions. We applied our results to establish the existence of a solution for some integralitions. Finally, an example is presented to clarify our theorem.
International Journal of Advanced Research in Science, Communication and Technology, 2022
In this paper, we defined a general form of the type of Suzuki functions on h-metric space to obt... more In this paper, we defined a general form of the type of Suzuki functions on h-metric space to obtain a common fixed point. Our results generalized some results from the literature.
Journal of Mathematical Analysis and Modeling
In this paper, the interpolative Caristi type weakly compatible contractive in a complete metric ... more In this paper, the interpolative Caristi type weakly compatible contractive in a complete metric space is applied to show some common fixed points results related to such mappings. Our application shows that the function which is used to prove the obtained results is a bounded map. An example is provided to show the useability of the acquired results.
Journal of mathematical analysis and modeling, Jun 30, 2021
In this paper, we investigate the existence and uniqueness of positive solutions for a class of C... more In this paper, we investigate the existence and uniqueness of positive solutions for a class of Caputotype fractional differential equations with nonlocal integral boundary conditions. Our analysis based on constructing the upper and lower control functions of the nonlinear terms without having any monotone conditions except the continuity, Green function, and Schauder&#39;s (Banach&#39;s) fixed point technique on a cone. Finally, some examples are given to substantiate our main results.
Journal of Mathematical Analysis and Modeling, 2020
In this paper, we conclude that $n$-linear functionals spaces $\Im$ has approximate fixed points ... more In this paper, we conclude that $n$-linear functionals spaces $\Im$ has approximate fixed points set, where $\Im$ is a non-empty bounded subset of an $n$-Banach space $H$ under the condition of equivalence, and we also use class of $(\mu,\sigma)$-nonexpansive mappings.
Advances in the Theory of Nonlinear Analysis and its Application, 2020
In this research paper, the nonlinear fractional relaxation equation involving the generalized Ca... more In this research paper, the nonlinear fractional relaxation equation involving the generalized Caputo derivative is reduced to an equivalent integral equation via the generalized Laplace transform. Moreover, the upper and lower solutions method combined with some fixed point theorems, and the properties of the Mittag-Leffler function are applied to investigate the existence and uniqueness of positive solutions for the problem at hand. At the end, to illustrate our results, we give an example.
Journal of Computer and Mathematical Sciences, 2019
In this paper, some theorems concerning the existence and uniqueness of fixed point in complete m... more In this paper, some theorems concerning the existence and uniqueness of fixed point in complete metric space are established. The results of the continuity clause we reached are introduced and some of the results we obtained are circulated.
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Papers by Basel M. Hardan