6 papers
Remarks on the paper "Treatment of Set-Valued Robustness via Separation and Scalarization"
Abhik Digar, Kuntal Som
In this paper, we remark on the published paper "Treatment of Set-Valued Robustness via Separation and Scalarization" [1], which deals with the robust solution to an uncertain cons…
Best approximations in metric spaces with property strongly UC
Abhik Digar
In this article, we introduce a geometrical notion, property strongly UC which is stronger than property UC and prove the existence of best approximations for a new class of almost…
Characterizations of strictly convex spaces and proximal uniform normal structure
Abhik Digar, G. Sankara Raju Kosuru
We provide a few characterizations of a strictly convex Banach space. Using this we improve the main theorem of [Digar, Abhik; Kosuru, G. Sankara Raju; Cyclic uniform Lipschitzian…
On proximal uniform normal structure and relatively nonexpansive mappings
Abhik Digar, G. Sankara Raju Kosuru
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 rel…
A Characterization of Weak Proximal Normal Structure and Best Proximity Pairs
Abhik Digar, Rafael Espínola García, G. Sankara Raju Kosuru
The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. {\bf{vol 463(2…
Global optimization on a metric space with a graph and an application to PBVP
Abhik Digar, G. S. Raju K
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…