Krasnoselskii type theorems in product Banach spaces and applications to systems of nonlinear transport equations and mixed fractional differential equations

Abstract

In this paper, we use a new technique for the treatment of systems based on the advantage of vector-valued norms and of the weak topology. We first present vector versions of the Leray-Schauder alternative and then some Krasnoselskii type fixed point theorems for a sum of two mappings. Applications are given to a system of nonlinear transport equations, and systems of mixed fractional differential equations.

Authors

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Sana Hadj Amor
Department of Mathematics, LR 11 ES 35, Higher School of Science and Technology, University of Sousse, Tunisia

Abdelhak Traiki
Department of Mathematics, LR 11 ES 35, Higher School of Science and Technology, University of Sousse, Tunisia

Keywords

Krasnoselskii fixed point theorem for a sum of operators; weak topology; generalized contraction; product Banach space; vector-valued norm; system of nonlinear transport equations; convergent to zero matrix; fractional integral.

Paper coordinates

Sana Hadj Amor, Radu Precup and Abdelhak Traiki, Krasnoselskii type theorems in product Banach spaces and applications to systems of nonlinear transport equations and mixed fractional differential equations, Fixed Point Theory, vol 23 (2022) no. 1, 105-126, https://doi.org/10.24193/fpt-ro.2022.1.07

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About this paper

Journal

Fixed Point Theory

Publisher Name

Department of Mathematics, ”Babeș-Bolyai” Cluj-Napoca, Romania

Print ISSN

15835022

Online ISSN

20669208

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