Nonlinear alternatives of hybrid type for nonself vector-valued maps and application

Abstract


In this paper we obtain nonlinear alternatives of Leray-Schauder and Monch type for nonself vector-valued operators, under hybrid conditions of Perov contraction and compactness.

Thus, we give vector versions of the theorems of Krasnosel’skii, Avramescu, Burton-Kirk and Gao-Li Zhang. An application is given to a boundary value problem for a system of second order differential equations in which some of the equations are implicit.

Authors

Veronica Ilea
Babes–Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania

Adela Novac
Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania

Diana Otrocol
Technical University of Cluj-Napoca, Department of Mathematics,  Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

Nonlinear operator; nonself map; fixed point; Perov contraction; nonlinear boundary value problem.

Paper coordinates

V. Ilea, A. Novac, D. Otrocol, R. Precup, Nonlinear alternatives of hybrid type for nonself vector-valued maps and application, Fixed Point Theory, 24 (2023) no. 1, 221-232, http://doi.org/10.24193/fpt-ro.2023.1.11

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About this paper

Journal

Fixed Point Theory

Publisher Name

Casa Cărţii de Ştiinţă Cluj-Napoca
(House of the Book of Science Cluj-Napoca)

Print ISSN

1583-5022

Online ISSN

2066-9208

google scholar link

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2023

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