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Research Article | Open Access

Existence and uniqueness of a positive solutions for the product of operators

Golnaz Pakgalb1, Mohammad Jahangiri Rad1( ), Ali Salimi Shamloo2, Majid Derafshpour1
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran
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Abstract

In this paper, we prove the existence of a positive solution for some equations involving multiplication of concave (possibly nonlinear) operators. Also, we provide a successively sequence to approximate the solution for such equations. This kind of the solution is necessary for quadratic differential and integral equations.

Keywords

fixed pointproduct of operatorquadratic integral equationpositive solutionconcave operator
CLC number: 47H10, 35B09, 45G10, 47N20

References

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AIMS Mathematics
Volume 7 Issue 10,
October 2022
Pages 18853-18869
DOI: 10.3934/math.20221038

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Cite this article:
Pakgalb G, Rad MJ, Shamloo AS, et al. Existence and uniqueness of a positive solutions for the product of operators. AIMS Mathematics, 2022, 7(10): 18853-18869. https://doi.org/10.3934/math.20221038

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Received: 08 June 2022
Revised: 17 August 2022
Accepted: 17 August 2022
Published: 15 October 2022
©2022 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)