Non-solid cone <i>b</i>-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 new convergence for sequences in cone b b -metric spaces over Banach algebras and completeness such spaces, namely, wrtn-completeness, are introduced. Under condition that wrtn-complete cones normal, we establish common fixed point theorem contractive conditions with vector-valued coefficients non-solid algebras, where s ≥ 1 s\ge 1 . As consequences, obtain number theorems contractions coefficients, especially versions contraction principle, Kannan’s Chatterjea’s algebras. Moreover, some valid examples presented to support our main results.