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