Fixed point results for almost nonexpansive mappings in $b$-metric spaces

Author:

Goswami NilakshiORCID,Haokip NehjamangORCID

Abstract

The aim of this paper is to introduce a new class of mappings called almost nonexpansive mappings in a $b$-metric space. Some characteristics of this class of mappings are discussed. Fixed point and common fixed point results for such mappings are obtained. An application to the Cauchy problem in a Banach space is also shown in this paper.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference24 articles.

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2. M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ “Babes-Bolyai” Mathematica LIV (3), 1–14, (2009).

3. F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proceedings of the National Academy of Sciences of the United States of America 54 (4), 1041–1044, (1965).

4. F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (3), 571–575, (1966).

5. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1, 5–11, (1993).

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