An extension of Krasnoselskii's cone fixed point theorem for a sum of two operators and applications to nonlinear boundary value problems

Author:

Benzenati Lyna, ,Mebarki Karima, ,

Abstract

"The purpose of this work is to establish a new generalized form of the Krasnoselskii type compression-expansion fixed point theorem for a sum of an expansive operator and a completely continuous one. Applications to three non- linear boundary value problems associated to second order differential equations of coincidence type are included to illustrate the main results."

Publisher

Babes-Bolyai University

Subject

General Mathematics

Reference18 articles.

1. "[1] Anderson, D.R., Avery, R.I., Fixed point theorem of cone expansion and compression of functional type, J. Difference Equ. Appl., 8(2002), no. 11, 1073-1083.

2. [2] Avery, R.I., Anderson, D.R., Krueger, R.J., An extension of the fixed point theorem of cone expansion and compression of functional type, Comm. Appl. Nonlinear Anal., 13(2006), no. 1, 15-26.

3. [3] Benzenati, L., Mebarki, K., Multiple positive fixed points for the sum of expansive mappings and k-set contractions, Math. Methods Appl. Sci., 42(2019), no. 13, 4412-4426.

4. [4] Benzenati, L., Mebarki, K., Precup, R., A vector version of the fixed-point theorem of cone compression and expansion for a sum of two operators, Nonlinear Studies, 27(2020), no. 3, 563-575.

5. [5] Deimling, K., Nonlinear Functional Analysis, Springer-Verlag, Berlin, Heidelberg, 1985.

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