First and foremost I offer my sincerest gratitude to my supervisor Dr.Tanmoy Paul, who has suppor... more First and foremost I offer my sincerest gratitude to my supervisor Dr.Tanmoy Paul, who has supported me throughout my thesis with his patience and knowledge. Without him this thesis would not have been completed.I also want to thank Dr. D.Sukumar and Dr. Venku Naidu Dogga for encouraging me. And I would like to thank some of our Ph.D scholars for helping me.
In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a m... more In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a metric space with a graph and prove best proximity points results for the same. Also, we demonstrate that the number of such points is same with the number of connected subgraphs. Hereafter, we introduce a fixed point mapping obtained from the aforesaid cyclic contraction and prove some fixed point theorems which will be used to find a common solution for a system of periodic boundary value problems. Our results unify and subsume many existing results in the literature
The main objective of this article is to provide an alternative approach to the central result of... more The main objective of this article is to provide an alternative approach to the central result of [Eldred, A. Anthony, Kirk, W. A., Veeramani, P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., vol 171(3), (2005) 283-293] using proximal uniform normal structure. Also we provide characterizations of a strictly convex space. Finally, sufficient conditions for the existence of a nonempty proximal sub-pair for a pair in a Banach space are discussed.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
We give a characterization of weak proximal normal structure using best proximity pair property. ... more We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove the existence of a best proximity pair in the setting of reflexive Banach spaces.
Numerical Functional Analysis and Optimization, 2020
A new class of mappings, called relatively continuous, is introduced and incorporated to elicit b... more A new class of mappings, called relatively continuous, is introduced and incorporated to elicit best proximity pair theorems for a non-self-mapping in the setting of reflexive Banach space. As a consequence we obtain a generalization of Carathéodory extension theorem for an initial value problem with L 1 functions on the right hand side.
First and foremost I offer my sincerest gratitude to my supervisor Dr.Tanmoy Paul, who has suppor... more First and foremost I offer my sincerest gratitude to my supervisor Dr.Tanmoy Paul, who has supported me throughout my thesis with his patience and knowledge. Without him this thesis would not have been completed.I also want to thank Dr. D.Sukumar and Dr. Venku Naidu Dogga for encouraging me. And I would like to thank some of our Ph.D scholars for helping me.
In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a m... more In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a metric space with a graph and prove best proximity points results for the same. Also, we demonstrate that the number of such points is same with the number of connected subgraphs. Hereafter, we introduce a fixed point mapping obtained from the aforesaid cyclic contraction and prove some fixed point theorems which will be used to find a common solution for a system of periodic boundary value problems. Our results unify and subsume many existing results in the literature
The main objective of this article is to provide an alternative approach to the central result of... more The main objective of this article is to provide an alternative approach to the central result of [Eldred, A. Anthony, Kirk, W. A., Veeramani, P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., vol 171(3), (2005) 283-293] using proximal uniform normal structure. Also we provide characterizations of a strictly convex space. Finally, sufficient conditions for the existence of a nonempty proximal sub-pair for a pair in a Banach space are discussed.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
We give a characterization of weak proximal normal structure using best proximity pair property. ... more We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove the existence of a best proximity pair in the setting of reflexive Banach spaces.
Numerical Functional Analysis and Optimization, 2020
A new class of mappings, called relatively continuous, is introduced and incorporated to elicit b... more A new class of mappings, called relatively continuous, is introduced and incorporated to elicit best proximity pair theorems for a non-self-mapping in the setting of reflexive Banach space. As a consequence we obtain a generalization of Carathéodory extension theorem for an initial value problem with L 1 functions on the right hand side.
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Papers by Abhik Digar