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 b b -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 b b -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 b b -metric spaces over Banach algebras, where the coefficients s ≥ 1 s\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 b b -metric spaces over Banach algebras. Moreover, some valid examples are presented to support our main results.