New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras (Analysis in Theory and Applications, 2022)
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 themappings should be continuous. Furthermore, the existence and the uniqueness of thefixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examplesand an application are given to support our new results.
Keywords: Cone $b$-metric spaces over Banach algebras; generalized $c$-distance; non-normal cone; generalized Lipschitz mappings; fixed point theorems.