Common fixed point and coincidence point results for generalized $ \alpha $-$ \varphi_{E} $-Geraghty contraction mappings in $ b $-metric spaces

Abstract

In this paper, we study the existence and uniqueness of common fixed point of $ \alpha_{i, j} $-$ \varphi_{{E}_{M, N}} $-Geraghty contraction mappings and the existence of coincidence point of $ \alpha_{i, j} $-$ \varphi_{E_N} $-Geraghty contraction mapping in the framework of $ b $-metric spaces. We also give two examples to support our results.

Keywords

• common fixed point
• coincidence point
• b-metric
• α_{i
• j}-φe_{m
• n}-geraghty contraction mappings
• j</sub>-φe_n-geraghty contraction mapping