Some Geometric Characterizations of a Fractional Banach Set

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:68 Issue:1
Some Geometric Characterizations of a Fractional Banach Set

Some Geometric Characterizations of a Fractional Banach Set

Pages : 546-558

View : 18 | Download : 11

Publication Date : 2019-02-01

Article Type : Research Paper

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, $insert ignore into journalissuearticles values( \beta );$, $ insert ignore into journalissuearticles values(L); $ and $ insert ignore into journalissuearticles values(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.
Keywords : reflexivity, convexity, fixed point property, approximative compactness

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