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Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle for Set Valued Mapping using the LZ-functions

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 158 - Number 2
Year of Publication: 2017
Authors:
Samih Lazaiz, Mohamed Aamri, Omar Zakary
10.5120/ijca2017912755

Samih Lazaiz, Mohamed Aamri and Omar Zakary. Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle for Set Valued Mapping using the LZ-functions. International Journal of Computer Applications 158(2):1-6, January 2017. BibTeX

@article{10.5120/ijca2017912755,
	author = {Samih Lazaiz and Mohamed Aamri and Omar Zakary},
	title = {Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle for Set Valued Mapping using the LZ-functions},
	journal = {International Journal of Computer Applications},
	issue_date = {January 2017},
	volume = {158},
	number = {2},
	month = {Jan},
	year = {2017},
	issn = {0975-8887},
	pages = {1-6},
	numpages = {6},
	url = {http://www.ijcaonline.org/archives/volume158/number2/26877-2017912755},
	doi = {10.5120/ijca2017912755},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

The aims of this paper is to give some new theorems in the field of fixed point theory. For that, we establish a generalized result of Caristi’s fixed point theorem by introducing a new type of functions that will be called the LZ-functions. And since that theorem is equivalent to Ekeland’s variational principle, we derive also an "- variational-type principle, which generalizes the latter. As application, we study the existence of solution for a system of equilibrium problem.

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Keywords

Fixed point, Set valued map, LZ-function, Caristi, Ekeland