TY - JOUR T1 - New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras AU - Han , Yan AU - Xu , Shaoyuan JO - Analysis in Theory and Applications VL - 3 SP - 335 EP - 350 PY - 2022 DA - 2022/07 SN - 38 DO - http://doi.org/10.4208/ata.OA-2017-0080 UR - https://global-sci.org/intro/article_detail/ata/20805.html KW - Cone $b$-metric spaces over Banach algebras, generalized $c$-distance, non-normal cone, generalized Lipschitz mappings, fixed point theorems. AB -
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.