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

Golnaz Pakgalb; Mohammad Jahangiri Rad; Ali Salimi Shamloo; Majid Derafshpour; Golnaz Pakgalb; Mohammad Jahangiri Rad; Ali Salimi Shamloo; Majid Derafshpour

doi:10.3934/math.20221038

AIMS Mathematics

2022, Volume 7, Issue 10: 18853-18869. doi: 10.3934/math.20221038

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

1.
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2.
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran

Received: 08 June 2022 Revised: 17 August 2022 Accepted: 17 August 2022 Published: 25 August 2022
MSC : 47H10, 35B09, 45G10, 47N20

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.
- fixed point,
- product of operator,
- quadratic integral equation,
- positive solution,
- concave operator
Citation: Golnaz Pakgalb, Mohammad Jahangiri Rad, Ali Salimi Shamloo, Majid Derafshpour. Existence and uniqueness of a positive solutions for the product of operators[J]. AIMS Mathematics, 2022, 7(10): 18853-18869. doi: 10.3934/math.20221038

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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.

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