Some Geometric Characterizations of a Fractional Banach Set

Abstract

This paper is devoted to investigate the modular structure of a fractional Banach set of sequences and prove that this set is reflexive and convex and it possesses uniform Opial, $( \beta )$, $ (L) $ and $ (H) $ properties. The convexity of the set is investigated by the notion of extreme points. These properties play an important role both in the study of fixed point theory and in the geometric characterizations of the Banach sets of sequences. This study extends the scope of the fractional calculus and it is related with fixed point and approximation theories.