scholarly journals Generalized strongly vector equilibrium problem for set-valued mappings

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1783-1790 ◽  
Author(s):  
Rais Ahmad ◽  
Mijanur Rahaman
Keyword(s):  
Equilibrium Problem ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Fan Theorem ◽  
Set Valued Mappings ◽  
Vector Equilibrium

In this paper, we introduce and study a generalized strongly vector equilibrium problem for set-valued mappings in real Banach spaces. Using Minty type lemma and KKM-Fan theorem as basic tools, we prove existence theorems for generalized strongly vector equilibrium problem with and without monotonicity, respectively. Some examples are given.

scholarly journals Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tao Chen
Keyword(s):  
Saddle Point ◽  
Existence Theorem ◽  
Equilibrium Problem ◽  
Existence Result ◽  
Existence Theorems ◽  
Saddle Points ◽  
Vector Equilibrium Problem ◽  
Saddle Point Theorem ◽  
Vector Equilibrium ◽  
Vector Valued

A new existence result ofε-vector equilibrium problem is first obtained. Then, by using the existence theorem ofε-vector equilibrium problem, a weaklyε-cone saddle point theorem is also obtained for vector-valued mappings.

scholarly journals Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Adem Kılıçman ◽  
Rais Ahmad ◽  
Mijanur Rahaman
Keyword(s):  
Equilibrium Problem ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Topological Vector Spaces ◽  
Fan Theorem ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Generalized Pseudomonotonicity

We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.

scholarly journals Existence theorems for generalized vector equilibria with variable ordering relation

2016 ◽  
Vol 47 (4) ◽  
pp. 455-475
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Strong Solutions ◽  
Existence Results ◽  
Reflexive Banach Spaces ◽  
Fan Theorem ◽  
Variable Ordering ◽  
Vector Equilibrium

In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

scholarly journals Existence and Duality of Generalized ε-Vector Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hong-Yong Fu ◽  
Bin Dan ◽  
Xiang-Yu Liu
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Kkm Theorem ◽  
Special Cases ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Vector Equilibrium

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems.

scholarly journals Extended Mixed Vector Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mijanur Rahaman ◽  
Adem Kılıçman ◽  
Rais Ahmad
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Fan Theorem ◽  
Noncompact Domain ◽  
Vector Equilibrium

We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005), some existence results for both problems are proved in noncompact domain.

scholarly journals Implicit vector equilibrium problems via nonlinear scalarisation

2005 ◽  
Vol 72 (1) ◽  
pp. 161-172 ◽  
Author(s):  
Jun Li ◽  
Nan-Jing Huang
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisation lemma and the FKKM theorem.

scholarly journals Extended f-Vector Equilibrium Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Khushbu ◽  
Zubair Khan
Keyword(s):  
Banach Space ◽  
Vector Space ◽  
Equilibrium Problem ◽  
Reflexive Banach Space ◽  
Vector Equilibrium Problem ◽  
Basic Tool ◽  
Fan Theorem ◽  
Hausdorff Topological Vector Space ◽  
Vector Equilibrium ◽  
Prove Existence Theorem

We introduce and study extended f-vector equilibrium problem. By using KKM-Fan Theorem as basic tool, we prove existence theorem in the setting of Hausdorff topological vector space and reflexive Banach space. Some examples are also given.

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