A variant of Banach’s contraction principle in ordered Banach spaces

Authors

  • Abdelhamid Benmezai National High School of Mathematics.

DOI:

https://doi.org/10.22199/issn.0717-6279-6128

Keywords:

Banach’s contraction principle, ordered Banach spaces, positive operators

Abstract

In this article we establish a version of Banach’s contraction principle in ordered Banach spaces. This version is adapted to prove existence and uniqueness results for an integral equation or a boundary value problem depending on the derivative.

References

P. B. Bailey, L. F. Shampine and P. E. Waltman, Nonlinear two point boundaryvalue problems, Academic Press, New York, London, 1968.

A. Benmezai, Krasnoselskii-type fixed point theorem in ordered Banach spaces and application to integral equations, Adv. Pure Appl. Math., 13 (2022), No.1, 50-61, DOI: 10.21494/ISTE.OP.2021.0759

A. Benmezai, Fixed point theorems in cones under local conditions, Fixed Point Theory, 18 (2017), No. 1, 107-126

A. Benmezai and N. Benkaci-Ali, Krein-Rutman operators and a variant of Banach contraction principle in ordered Banach spaces, Bull. Math. Soc. Sci. Math. Roumanie, 64 (2021), No. 3, 255-280.

A. Benmezai, B. Boucheneb, J. Henderson and S. Mechrouk, The index jump property for 1-hmogeneous positive maps and fixed point theorems in cones, J. Nonlinear Funct. Anal. 2017 (2017), Article ID 6.

S. R. Bernfeld and V. Lakshmikantham, Introduction to nonlinear boundary value problems, Academic Press, New York, London, 1974.

G. Darbo, Punti uniti in trasformazioni a codomio non compatto, Rend. Sem. Mat. Uni. Padova, 24(1955), 84-92.

K. Kuratowski, Sur les espaces completes, Fund. Math., 15 (1930), 301-209.

K. Yoshida, Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1980.

Published

2024-05-02

How to Cite

[1]
A. Benmezai, “A variant of Banach’s contraction principle in ordered Banach spaces”, Proyecciones (Antofagasta, On line), vol. 43, no. 3, pp. 555-569, May 2024.

Issue

Section

Artículos