Application to fixed point theory of α-θ-E-Geraghty Pata proximal contractions

Abstract

Here, we discuss the idea of α-θ-E-Geraghty Pata proximal contraction and weak ϕ-α-θ-E-Geraghty Pata proximal contraction by merging contraction criteria put forth by Pata and Geraghty utilizing the α-θ-proximal admissibility. In both standard as well as partially ordered metric spaces, for such proximal contractions, we present proximity point results for both single as well as multivalued mappings. We also investigate the existence of coupled fixed point for α-θ-E-Geraghty Pata type contractions in regular metric space. Numerous findings in the literature are generalized, expanded upon, and unified by these findings. We provide an application of fractional differential and few examples to demonstrate how outstanding our findings are. MSC Classification: 46T99 , 54E50 , 47H10 , 54H10