scholarly journals Vector Variational Inequalities In G-Convex Spaces

2021 ◽  
Vol 53 ◽  
Author(s):  
Maryam Salehnejad ◽  
Mahdi Azhini
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Kkm Theorem ◽  
Convex Spaces

Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces.

scholarly journals The KKM maps and fixed point theorems in convex spaces

2003 ◽  
Vol 34 (2) ◽  
pp. 169-174
Author(s):  
Polly W. Sy ◽  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Kkm Theorem ◽  
Approximate Fixed Point ◽  
Kkm Maps ◽  
New Form ◽  
Convex Spaces

From a general form of the celebrated Knaster--Kuratowski--Mazurkiewicz (simply, KKM) theorem, we deduce a new form of the Fan--Browder fixed point theorem, an approximate fixed point theorem, and the Himmelberg fixed point theorem.

scholarly journals Vector Variational-Like Inequalities with Generalized Semimonotone Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Suhel Ahmad Khan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Vector Variational Inequality ◽  
Inequality Problem

We introduce the concepts of generalized relaxed monotonicity and generalized relaxed semimonotonicity. We consider a class of generalized vector variationa-llike inequality problem involving generalized relaxed semimonotone mapping. By using Kakutani-Fan-Glicksberg’s fixed-point theorem, we prove the solvability for this class of vector variational-like inequality with relaxed monotonicity assumptions. The results presented in this paper generalize some known results for vector variational inequality in recent years.

scholarly journals Connectedness of Solution Sets for Weak Vector Variational Inequalities on Unbounded Closed Convex Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Ren-you Zhong ◽  
Yun-liang Wang ◽  
Jiang-hua Fan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Convex Sets ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Solution Set ◽  
Solution Sets ◽  
Finite Dimensional ◽  
Path Connectedness ◽  
Weak Vector

We study the connectedness of solution set for set-valued weak vector variational inequality in unbounded closed convex subsets of finite dimensional spaces, when the mapping involved is scalarC-pseudomonotone. Moreover, the path connectedness of solution set for set-valued weak vector variational inequality is established, when the mapping involved is strictly scalarC-pseudomonotone. The results presented in this paper generalize some known results by Cheng (2001), Lee et al. (1998), and Lee and Bu (2005).

scholarly journals An extension of a theorem of Sahab, Khan, and Sessa

2001 ◽  
Vol 27 (11) ◽  
pp. 701-706 ◽  
Author(s):  
A. R. Khan ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Invariant Approximation ◽  
Recent Theorem ◽  
Locally Convex ◽  
Convex Spaces

A fixed point theorem of Fisher and Sessa is generalized to locally convex spaces and the new result is applied to extend a recent theorem on invariant approximation of Sahab, Khan, and Sessa.

Some Fixed Point Theorems in Metrically Convex Spaces

2000 ◽  
Vol 7 (3) ◽  
pp. 523-530 ◽  
Author(s):  
M. S. Khan ◽  
H. K. Pathak ◽  
M. D. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Convex Metric Space ◽  
Convex Spaces

Abstract A fixed point theorem is proved in a complete metrically convex metric space. Our result generalizes the theorems of Assad [Tamkang J. Math. 7: 91–94, 1976] and Chatterjea [C.R. Acad., Bulgare Sci. 25: 727–730, 1972].

scholarly journals A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Haishu Lu ◽  
Qingwen Hu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Theorems ◽  
Abstract Economies ◽  
Collectively Fixed Point ◽  
Convex Spaces

The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.

scholarly journals A fixed point theorem in locally convex spaces

2010 ◽  
Vol 61 (2) ◽  
pp. 223-239 ◽  
Author(s):  
Vladimir Kozlov ◽  
Johan Thim ◽  
Bengt Ove Turesson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces
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