In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is intr... more In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.
In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontract... more In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontraction of integral type mappings in the context of orthogonal metric spaces and establish some fixed point results. We construct an example to show the existence of the new type of mappings introduce in this work. Our results substantially unify, generalize and complement the comparable results in the existing literature. As an application of our results, we derive periodic point results for the generalized single valued orthogonal α-F-contraction of integral type mappings in orthogonal metric spaces.
In this paper, we introduce the concept of a generalized α-Suzuki-Geraghty type contraction mappi... more In this paper, we introduce the concept of a generalized α-Suzuki-Geraghty type contraction mapping and obtain fixed point results in the framework of an f-orbitally complete b-metric space. The results proved herein improve, generalize, and unify various comparable results in the existing literature. Some examples are presented to validate the effectiveness and applicability of our main result. It is also shown that the presented results are proper extensions of corresponding results in the existing literature. As an application of our obtained result, we establish the existence of a solution of integral equations in the setup of b-metric spaces.
The second author is supported by Grant No. 174025 of the Ministry of Education, Science and Tech... more The second author is supported by Grant No. 174025 of the Ministry of Education, Science and Technological Development, Republic of Serbia.
In this paper, the concept of a new φ-generalized quasi metric space is introduced. A number of w... more In this paper, the concept of a new φ-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from φ-generalized quasi metric space. Some general fixed point theorems in a φ-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations. To the memory of Professor Lj. Ćirić (1935–2016)
Journal of Fixed Point Theory and Applications, 2017
In this paper, first, we define a partial order on a soft set (F, A) and introduce some related c... more In this paper, first, we define a partial order on a soft set (F, A) and introduce some related concepts. Then, using the concept of a soft mapping introduced by Babitha and Sunil (Comput Math Appl 60(7):1840–1849, 2010), a soft version of Knaster–Tarski fixed point theorem is obtained. Some examples are presented to support the concepts introduced and the results proved herein. As an application of our result, we show that the soft Knaster–Tarski fixed point theorem ensures the existence of a soft common fixed point for a commuting family of order-preserving soft mappings.
The National Research Foundation (NRF) and DST-NRF Centre of Excellence in Mathematical and Stati... more The National Research Foundation (NRF) and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).
We introduce the concepts of α-closed multivlaued mappings, an (α-ψ)-generalized rational contrac... more We introduce the concepts of α-closed multivlaued mappings, an (α-ψ)-generalized rational contraction multivalued mappings and then to establish the existence of common fixed points of such mappings in the setting of d-Cauchy complete semi-metric spaces. Some examples are presented to support the results proved herein. We also show that our results are applicable where the comparable existing results in the literature can not be applied. Our results generalize and extend various results in the existing literature. As an application of our results, the existence of common fixed points of single valued and multivalued mappings is proved in the framework of d-Cauchy complete semi-metric spaces endowed with an arbitrary binary relation R.
The third author is thankful to the financial assistance of the National Research Foundation (NRF... more The third author is thankful to the financial assistance of the National Research Foundation (NRF) and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).
In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is intr... more In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.
In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontract... more In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontraction of integral type mappings in the context of orthogonal metric spaces and establish some fixed point results. We construct an example to show the existence of the new type of mappings introduce in this work. Our results substantially unify, generalize and complement the comparable results in the existing literature. As an application of our results, we derive periodic point results for the generalized single valued orthogonal α-F-contraction of integral type mappings in orthogonal metric spaces.
In this paper, we introduce the concept of a generalized α-Suzuki-Geraghty type contraction mappi... more In this paper, we introduce the concept of a generalized α-Suzuki-Geraghty type contraction mapping and obtain fixed point results in the framework of an f-orbitally complete b-metric space. The results proved herein improve, generalize, and unify various comparable results in the existing literature. Some examples are presented to validate the effectiveness and applicability of our main result. It is also shown that the presented results are proper extensions of corresponding results in the existing literature. As an application of our obtained result, we establish the existence of a solution of integral equations in the setup of b-metric spaces.
The second author is supported by Grant No. 174025 of the Ministry of Education, Science and Tech... more The second author is supported by Grant No. 174025 of the Ministry of Education, Science and Technological Development, Republic of Serbia.
In this paper, the concept of a new φ-generalized quasi metric space is introduced. A number of w... more In this paper, the concept of a new φ-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from φ-generalized quasi metric space. Some general fixed point theorems in a φ-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations. To the memory of Professor Lj. Ćirić (1935–2016)
Journal of Fixed Point Theory and Applications, 2017
In this paper, first, we define a partial order on a soft set (F, A) and introduce some related c... more In this paper, first, we define a partial order on a soft set (F, A) and introduce some related concepts. Then, using the concept of a soft mapping introduced by Babitha and Sunil (Comput Math Appl 60(7):1840–1849, 2010), a soft version of Knaster–Tarski fixed point theorem is obtained. Some examples are presented to support the concepts introduced and the results proved herein. As an application of our result, we show that the soft Knaster–Tarski fixed point theorem ensures the existence of a soft common fixed point for a commuting family of order-preserving soft mappings.
The National Research Foundation (NRF) and DST-NRF Centre of Excellence in Mathematical and Stati... more The National Research Foundation (NRF) and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).
We introduce the concepts of α-closed multivlaued mappings, an (α-ψ)-generalized rational contrac... more We introduce the concepts of α-closed multivlaued mappings, an (α-ψ)-generalized rational contraction multivalued mappings and then to establish the existence of common fixed points of such mappings in the setting of d-Cauchy complete semi-metric spaces. Some examples are presented to support the results proved herein. We also show that our results are applicable where the comparable existing results in the literature can not be applied. Our results generalize and extend various results in the existing literature. As an application of our results, the existence of common fixed points of single valued and multivalued mappings is proved in the framework of d-Cauchy complete semi-metric spaces endowed with an arbitrary binary relation R.
The third author is thankful to the financial assistance of the National Research Foundation (NRF... more The third author is thankful to the financial assistance of the National Research Foundation (NRF) and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).
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