Abstract
Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.
Highlights
As a generalization of the metric space, Bakhtin [1] introduced the notion of b-metric space and since several papers have been published on the fixed point theory in such spaces
We will apply some of the extended fixed point results for Geraghty contractions in b-metric spaces, presented in ([3]), to a nonlinear Fredholm–Volterra integral equation with modified argument
In 2019, Faraji et al [3] obtained and published two fixed point theorems for Geraghty contraction on b-metric spaces and their applications, which we present below
Summary
As a generalization of the metric space, Bakhtin [1] introduced the notion of b-metric space and since several papers have been published on the fixed point theory in such spaces. Let ( X, d) be a b-metric space with coefficient s ≥ 1 and S denote the set of all functions α : [0, ∞) → [0, 1s ) that satisfy the following condition: lim α(tn ) =. Using these theorems, in 2019, Faraji et al [3] presented other fixed point results for Geraghty contraction in b-metric spaces and their applications to integral equations. In 2019, Faraji et al [3] presented other fixed point results for Geraghty contraction in b-metric spaces and their applications to integral equations We will apply some of the extended fixed point results for Geraghty contractions in b-metric spaces, presented in ([3]), to a nonlinear Fredholm–Volterra integral equation with modified argument
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