Common fixed and coincidence point theorems for nonlinear self-mappings in cone $ b $-metric spaces using $ \varphi $-mapping

Abstract

In this paper, by means of a mapping $ \varphi\in\Phi(P, P_1) $, some new common fixed and coincidence point theorems for four and six nonlinear self-mappings in cone $ b $-metric spaces are established, respectively. Also, some examples are given to prove the effectiveness of our results. And with some remarks stating that our results complement and sharply improve some related results in the literature.

Keywords

• coincidence point
• common fixed point
• $ \varphi $-mapping
• nonlinear contraction
• cone $ b $-metric space