Positive coincidence points for a class of nonlinear operators and their applications to matrix equations-Reference-Cited by-同舟云学术

Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

Published:2020-01-01 Issue:1 Volume:18 Page:858-872
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Kedim Imed¹,Berzig Maher²,Ajmi Ahdi Noomen¹

Affiliation:

1. Department of Mathematics, College of Science and Humanities in Al-Sulail , Prince Sattam bin Abdulaziz University , Saudi Arabia

2. Université de Tunis, Ecole Nationale Supérieure d’Ingénieurs de Tunis, Département de Mathématiques , 1008 Montfleury , Tunisie

Abstract

Abstract Consider an ordered Banach space and

f , g

f,g

two self-operators defined on the interior of its positive cone. In this article, we prove that the equation

f ( X ) = g ( X )

f(X)=g(X)

has a positive solution, whenever f is strictly

\alpha

-concave g-monotone or strictly

( − α )

(-\alpha )

-convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0049/pdf

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