Non-solid cone b-metric spaces over Banach algebras and fixed point results of contractions with vector-valued coefficients

Abstract

In this article, without requiring solidness of the underlying cone, a kind of new convergence for sequences in cone bb-metric spaces over Banach algebras and a new kind of completeness for such spaces, namely, wrtn-completeness, are introduced. Under the condition that the cone bb-metric spaces are wrtn-complete and the underlying cones are normal, we establish a common fixed point theorem of contractive conditions with vector-valued coefficients in the non-solid cone bb-metric spaces over Banach algebras, where the coefficients s≥1s\ge 1. As consequences, we obtain a number of fixed point theorems of contractions with vector-valued coefficients, especially the versions of Banach contraction principle, Kannan’s and Chatterjea’s fixed point theorems in non-solid cone bb-metric spaces over Banach algebras. Moreover, some valid examples are presented to support our main results.

Keywords

• non-solid cone b-metric spaces over banach algebras
• contractions with vector-valued coefficients
• coincidence point
• fixed point theorems
• wrtn-convergence and wrtn-completeness
• 47h10
• 54h25