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Research Article | Open Access

Some results on the space of bounded second κ-variation functions

Jurancy Ereú1, Luz E. Marchan2( ), Liliana Pérez2, Henry Rojas1
Departamento de Matemáticas, Decanato de Ciencias y Tecnología, Universidad Centroccidental Lisandro Alvarado, Barquisimeto, Estado Lara, Venezuela
Escuela Superior Politécnica del Litoral, ESPOL, Facultad de Ciencias Naturales y Matemáticas, Campus Gustavo Galindo Km 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador
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Abstract

In this paper, we prove that if a globally Lipschitz non-autonomous superposition operator maps the space of functions of bounded second κ-variation into itself then its generator function satisfies a Matkowski condition. We also provide conditions for the existence and uniqueness of solutions of the Hammerstein and Volterra equations in this space.

Keywords

superposition operatorintegral equationbounded second κ-variationHammersteinHammerstein-VolterraVolterra existence and uniqueness
CLC number: 45-XX, 45DXX, 47-XX, 47H30

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 21872-21892
DOI: 10.3934/math.20231115

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Cite this article:
Ereú J, Marchan LE, Pérez L, et al. Some results on the space of bounded second κ-variation functions. AIMS Mathematics, 2023, 8(9): 21872-21892. https://doi.org/10.3934/math.20231115

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Received: 16 March 2023
Revised: 18 June 2023
Accepted: 25 June 2023
Published: 15 September 2023
©2023 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)