## 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

## About this paper

##### Journal

Fixed Point Theory

##### Publisher Name

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

##### Print ISSN

15835022

##### Online ISSN

20669208

google scholar link

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