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



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


	Fixed Point Theory, Volume 23, No. 1, 2022, 105-126, February 1st, 2022 DOI: 10.24193/fpt-ro.2022.1.07 Authors: Sana Hadj Amor, Radu Precup and Abdelhak Traiki 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. Key Words and Phrases: 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. 2010 Mathematics Subject Classification: 47B38, 47H09, 47H08, 47H10. Published on-line: February 1st, 2022. Abstract pdf Fulltext pdf Back to volume's table of contents