New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras
Year: 2022
Author: Yan Han, Shaoyuan Xu
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 3 : pp. 335–350
Abstract
In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2017-0080
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 3 : pp. 335–350
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Cone $b$-metric spaces over Banach algebras generalized $c$-distance non-normal cone generalized Lipschitz mappings fixed point theorems.