New iterative scheme for fixed point results of weakly compatible maps in multiplicative GM−metric space via various contractions with application

Abstract

In this manuscript, we induced several vivid common fixed point theorems for four maps in the setting of complete multiplicative $ {G_{\boldsymbol{M}}}- $metric space via various contractive conditions such as $ \Delta $-implicit contractions. Some new definitions and results are introduced in multiplicative $ {G_{\boldsymbol{M}}}- $ metric space.Moreover, illustrative examples are given to validate our obtained results and an application to a system of nonlinear integral equations are provided to show the novelty of our new results.

Keywords

• fixed point
• multiplicative g_m−metric space
• point of coincidence
• weakly compatible maps
• δ-implicit contractions