### Solutions of Mixed Integral Equations via Hybrid Contractions

#### Keywords:

fixed point, metric space, θ-contraction, nonlinear integral equation#### Abstract

This paper establishes certain new fixed point results for a class of contractions known as admissible hybrid (θ-ζ)-contraction within the context of rectangular metric space. The main contribution of this work is a straightforward unification of the notions of admissible mappings, θ-contractions, and the contraction mapping principle. As a result, several corollaries are inferred from the primary findings given here, some of which comprise some previously disclosed concepts. An application to one of the obtained results is the proposal of new criteria for the existence and uniqueness of a solution to a mixed nonlinear fixed point problem, using Volterra-Fredholm integrals. Nontrivial analytical and numerical examples are given and compared with the specific articles supporting this study in order to elucidate the underlying theoretical ideas.

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*Advances in the Theory of Nonlinear Analysis and Its Application*,

*7*(5), 165-182. https://doi.org/10.17762/atnaa.v7.i5.333