Korean J. Math. Vol. 30 No. 4 (2022) pp.603-614
DOI: https://doi.org/10.11568/kjm.2022.30.4.603

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

Main Article Content

Surjeet Singh Chauhan(Gonder)
Kanika Rana
Mohammad Asim
Mohammad Imdad


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.

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