Common fixed points for two pairs of selfmaps satisfying certain contraction condition in $b$-metric spaces

Abstract

This study introduces generalized contraction for two pairs of selfmaps in complete $b$-metric spaces, and it then establishes the existence of common fixed points under the presumptions that these two pairs of maps are weakly compatible and satisfy the condition for generalized contraction. A sequence of selfmaps is added as an extension of the same. Additionally, we demonstrate the same using various hypotheses on two pairs of selfmaps that satisfy the $b$-(E.A)-property. Some of the conclusions in the literature are extended /generalized to two pairs of self maps by our theorems.