A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras

Year 2019, Volume: 4 Issue: 1, 11 - 18, 15.04.2019

Faruk Develi , Muttalip Özavşar Stojan Radenovic

https://doi.org/10.30931/jetas.510813

https://izlik.org/JA84UL84HN

Abstract

In this paper, we first consider Nadler type contractions with the
generalized Lipschitz constant k holding r(k)<1 instead of r(sk)<1
where r(k) is the spectral radius of k and s≥1 is the coefficient
of the underlying cone b-metric spaces over Banach algebras. Then, we
prove the corresponding fixed point theorem for such mappings. Finally, we
compare our result with one obtained by the case r(sk)<1 by introducing
some proper examples.

Keywords

Nadler Mappings; Banach Algebra; Cone b-Metric

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