# Some Fixed Point Results on \((\alpha,\beta)\)-\(H\)-\(\varphi\)-Contraction Mappings in Partial Metric Spaces With Application

## DOI:

https://doi.org/10.26713/cma.v15i1.2491## Keywords:

\(H\)-\(\varphi\)-contraction mapping, Generalized \(H\)-\(\varphi\)-contraction mapping, \((\alpha, \beta)\)-\(H\)-\(\varphi\)-contraction mapping, Partial metric spaces## Abstract

In this paper, we introduce the notion of \(H\)-\(\varphi\)-contraction, generalized \(H\)-\(\varphi\)-contraction, \((\alpha,\beta)\)-\(H\)-\(\varphi\)-contraction mappings and establish some fixed point results for such mappings in the context of partial metric spaces. An example is presented to illustrate the validity of the results.\ Further, the existence of the solution of nonlinear integral equation is discussed as an application of the result.

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*Communications in Mathematics and Applications*,

*15*(1), 133–144. https://doi.org/10.26713/cma.v15i1.2491

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