Fixed point theorems for b-generalized contractive mappings with weak continuity conditions

Abstract

The purpose of this paper was to introduce several $ b $-generalized contractive mappings in the framework of cone $ b $-metric spaces over Banach algebras. The obtained contractions generalized and extended the counterparts in metric spaces, cone metric spaces, and $ b $-metric spaces. Moreover, via weakening the completeness of the spaces, we gave some fixed point theorems for asymptotically regular mappings without considering the orbital continuity and $ k $-continuity of the mappings. Those who need a specification is our results do not rely on the continuity of $ b $-metric and the normality of cones. In addition, some nontrivial examples were presented to illustrate the superiority of our fixed point theorems.

Keywords

• fixed point
• kannan type contraction
• asymptotic regularity
• weak orbital continuity
• k-continuity