# Geraghty type contractions in $b-$metric-like spaces

## Main Article Content

## Abstract

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in $b-$metric-like spaces, which remains an extended version of corresponding results in $b-$metric spaces and metric-like spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in $b-$metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in $b-$metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.

## Article Details

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