Existence of Best Proximity Pairs and a Generalization of Carathéodory Theorem. (8th December 2020) - Digar, Abhik; Kosuru, G. Sankara Raju
Abstract: 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.