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BINAYAK S. CHOUDHURY,Pulak Konar,Nikhilesh Metiya 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.1
In this paper we prove certain coupled coincidence point and coupled common xed point results in partially ordered metric spaces for a pair of compatible mappings which satisfy certain rational inequality. The results are supported with two examples.
EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS
Bhavana Deshpande,Amrish Handa,Shamim Ahmad Thoker 영남수학회 2016 East Asian mathematical journal Vol.32 No.3
We present coincidence point theorem for g-non-decreasing mappingssatisfying generalized nonlinear contraction on partially ordered metricspaces. We show how multidimensional results can be seen as simpleconsequences of our unidimensional coincidence point theorem. We also obtainthe coupled coincidence point theorem for generalized compatible pair ofmappings F, G : X2 → X by using obtained coincidence pointresults. Furthermore, an example and an application to integral equation arealso given to show the usability of obtained results. Our resultsgeneralize, modify, improve and sharpen several well-known results.
Amrish Handa 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.3
We introduce (CLRg) property for hybrid pair F : X×X→2^X and g : X→X. We also introduce joint common limit range (JCLR) property for two hybrid pairs F,G : X×X→2^X and f, g : X→X. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (,,)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.
HUGE COUPLED COINCIDENCE POINT THEOREM FOR GENERALIZED COMPATIBLE PAIR OF MAPPINGS WITH APPLICATIONS
Bhavana Deshpande,Amrish Handa 한국수학교육학회 2016 純粹 및 應用數學 Vol.23 No.1
We establish a coupled coincidence point theorem for generalized com- patible pair of mappings under generalized nonlinear contraction on a partially or- dered metric space. We also deduce certain coupled ffixed point results without mixed monotone property of F : X £ X ! X : An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results. We establish a coupled coincidence point theorem for generalized com- patible pair of mappings under generalized nonlinear contraction on a partially or- dered metric space. We also deduce certain coupled fixed point results without mixed monotone property of F : X £ X ! X : An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.
HUGE CONTRACTION ON PARTIALLY ORDERED METRIC SPACES
Bhavana Deshpande,Amrish Handa,Chetna Kothari 한국수학교육학회 2016 純粹 및 應用數學 Vol.23 No.1
We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G:X²→X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.
Bhavana Deshpande,Amrish Handa 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.3
We establish a common coupled ¯xed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to ¯nd coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.
EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS
Deshpande, Bhavana,Handa, Amrish,Thoker, Shamim Ahmad The Youngnam Mathematical Society 2016 East Asian mathematical journal Vol.32 No.3
We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.
CHOUDHURY, BINAYAK S.,KONAR, PULAK,METIYA, NIKHILESH The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.1
In this paper we prove certain coupled coincidence point and coupled common fixed point results in partially ordered metric spaces for a pair of compatible mappings which satisfy certain rational inequality. The results are supported with two examples.
COMMON COUPLED COINCIDENCE POINT RESULTS FOR TWO MAPS IN CONE b-METRIC SPACES OVER BANACH ALGEBRAS
Yang Young-Oh 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.1
In this paper, we obtain several common coupled coincidence point results and coupled fixed point results for two mappings satisfying certain contractive condition on complete cone b-metric spaces over Banach algebra, using the properties of spectral radiuses. Also we give two simple examples and obtain the existence and uniqueness of solution for some equations by using our results.
Bhavana Deshpande,Sushil Sharma,Amrish Handa 한국수학교육학회 2013 純粹 및 應用數學 Vol.20 No.3
We establish a common fixed point theorem for mappings under ∅-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.