Fixed point results for dominated mappings in rectangular b-metric spaces with applications

Abstract

In this paper, we establish some fixed point results for α-dominated mappings fulfilling new generalized locally Ćirić type rational contraction conditions in complete rectangular b-metric space. As an application, we establish the existence of fixed point of $\preceq $-dominated mappings in an ordered complete rectangular b-metric space. The notion of graph dominated mappings is introduced. Fixed point results with graphic contractions for such mappings are established.

Keywords

• fixed point
• complete rectangular <i>b</i>-metric space
• <i>α</i>-dominated mapping
• ćirić type rational contraction condition
• partial order
• $\preceq$-dominated mapping
• graph dominated mapping