Ekeland type variational principle with applications to quasi-variational inclusion problems

Lai Jiu Lin; Chih Sheng Chuang; Suliman Al-Homidan

doi:10.1016/j.na.2009.07.038

Ekeland type variational principle with applications to quasi-variational inclusion problems

Lai Jiu Lin^*
, Chih Sheng Chuang
, Suliman Al-Homidan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces.

Original language	English
Pages (from-to)	651-661
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	72
Issue number	2
DOIs	https://doi.org/10.1016/j.na.2009.07.038
State	Published - 15 Jan 2009

Bibliographical note

Funding Information:
In this research, the first and the second authors were supported by the National Science Council of the Republic of China, and the third author was partially supported by the SABIC/Fast Track Research Project No. # SB080004 of King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia. Authors are grateful to the referee for his/her valuable comments and suggestions to improve the previous draft of this paper.

Keywords

Caristi-Kirk type fixed point theorem
Ekeland type variational principle
Lower semicontinuity
Quasi-equilibrium problems
Quasi-optimization problems
Quasi-variational inclusion problems
Sequentially lower monotone maps
Uniformly spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2009.07.038

Cite this

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title = "Ekeland type variational principle with applications to quasi-variational inclusion problems",

abstract = "In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces.",

keywords = "Caristi-Kirk type fixed point theorem, Ekeland type variational principle, Lower semicontinuity, Quasi-equilibrium problems, Quasi-optimization problems, Quasi-variational inclusion problems, Sequentially lower monotone maps, Uniformly spaces",

author = "Lin, \{Lai Jiu\} and Chuang, \{Chih Sheng\} and Suliman Al-Homidan",

note = "Funding Information: In this research, the first and the second authors were supported by the National Science Council of the Republic of China, and the third author was partially supported by the SABIC/Fast Track Research Project No. \# SB080004 of King Fahd University of Petroleum \& Minerals, Dhahran, Saudi Arabia. Authors are grateful to the referee for his/her valuable comments and suggestions to improve the previous draft of this paper.",

year = "2009",

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doi = "10.1016/j.na.2009.07.038",

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T1 - Ekeland type variational principle with applications to quasi-variational inclusion problems

AU - Lin, Lai Jiu

AU - Chuang, Chih Sheng

AU - Al-Homidan, Suliman

N1 - Funding Information: In this research, the first and the second authors were supported by the National Science Council of the Republic of China, and the third author was partially supported by the SABIC/Fast Track Research Project No. # SB080004 of King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia. Authors are grateful to the referee for his/her valuable comments and suggestions to improve the previous draft of this paper.

PY - 2009/1/15

Y1 - 2009/1/15

N2 - In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces.

AB - In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces.

KW - Caristi-Kirk type fixed point theorem

KW - Ekeland type variational principle

KW - Lower semicontinuity

KW - Quasi-equilibrium problems

KW - Quasi-optimization problems

KW - Quasi-variational inclusion problems

KW - Sequentially lower monotone maps

KW - Uniformly spaces

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DO - 10.1016/j.na.2009.07.038

M3 - Article

AN - SCOPUS:71649098304

SN - 0362-546X

VL - 72

SP - 651

EP - 661

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 2

ER -

Ekeland type variational principle with applications to quasi-variational inclusion problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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