Compatible mappings and its variants for generalized ψ-∅-weak contraction condition

Abstract

In the present paper, first we introduce generalized ψ-∅-weak contraction condition that involves cubic and quadratic terms of distance function d(x,y) and then proved common fixed point theorems for compatible mappings. Secondly, we deal with variants of compatible mappings type (K), type (R) and type (E). At the end, we provide applications of our results.