A Novel Framework of Complex-Valued Controlled S-Metric Spaces and Its Applications to Nonlinear Integral Equations

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DOI: https://doi.org/10.28924/2291-8639-24-2026-196
Published: Jun 22, 2026
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Haitham Qawaqneh, Gawhara Al-Musannef, Habes Alsamir, A Novel Framework of Complex-Valued Controlled S-Metric Spaces and Its Applications to Nonlinear Integral Equations, Int. J. Anal. Appl., 24 (2026), 196.

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Haitham Qawaqneh, Gawhara Al-Musannef, Habes Alsamir

Abstract

In this work, we introduce the framework of complex-valued modulated \(S\)-metric structures, which unifies and extends several earlier notions such as controlled \(S\)-metrics and complex-valued \(S_b\)-metrics. The proposed setting provides a richer environment for establishing fixed point principles. Within this context, we obtain new fixed point theorems, supported by illustrative examples, and show how many existing results appear as particular consequences of our findings. As a practical demonstration, we apply the developed theory to prove the existence of solutions for a class of nonlinear Volterra integral equations.

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