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 - <p style="text-align: justify;">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.</p>