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Research Article | Open Access

Solutions to Volterra integral equations in bounded Φ-variation spaces

Mireya Bracamonte( ), Liliana Pérez
Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, ESPOL, Campus Gustavo Galindo Km. 30.5 Vía Perimetral, 090902, Ecuador
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Abstract

This article examines the existence of solutions to a Volterra-type integral equation in the space of functions of bounded Φ-variation. Conditions on the given functions are established to guarantee the existence of such solutions. Furthermore, it is shown that any two solutions are equal almost everywhere. The possibility of extending solutions to larger intervals is also explored.

Keywords

Volterra integralΦ-bounded variation
CLC number: 26A45, 45D05

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 9126-9145
DOI: 10.3934/math.2026376

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Cite this article:
Bracamonte M, Pérez L. Solutions to Volterra integral equations in bounded Φ-variation spaces. AIMS Mathematics, 2026, 11(4): 9126-9145. https://doi.org/10.3934/math.2026376

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Received: 15 December 2025
Revised: 11 March 2026
Accepted: 24 March 2026
Published: 02 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)