Fixed Points of a New Geraghty Contraction

Abstract

In this paper, we introduce a new type of (α, β)-ψ-Geraghty rational contraction in b-metric space by generalizing alpha-psi-contraction with (α,β)-admissible mapping. Further, we prove some new fixed point theorems for this new (α, β)-ψ- Geraghty rational contraction. Some examples are illustrated for the suitability of the result. Further, we apply our results in solving integral equation.