scholarly journals A New Fixed Point Theorem and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Min Fang ◽  
Xie Ping Ding
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Topological Space ◽  
Point Theorem ◽  
Kkm Theorem ◽  
Minimax Inequalities ◽  
Convexity Structure ◽  
Ky Fan

A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space) without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.

scholarly journals On minimax inequalities on spaces having certain contractible subsets

1993 ◽  
Vol 47 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Minimax Theorem ◽  
Saddle Point Theorem ◽  
Minimax Inequalities ◽  
Von Neumann ◽  
Matching Theorem ◽  
Quasi Variational Inequality ◽  
Ky Fan

The concept of a convex space is extended to an H-space; that is, a space having certain family of contractible subsets. For such spaces the KKM type theorems, the Fan-Browder fixed point theorem, the Ky Fan type matching theorem, and minimax inequalities are given. Moreover, applications to a von Neumann-Sion type minimax theorem, a saddle point theorem, a quasi-variational inequality, and a Kakutani type fixed point theorem are obtained.

scholarly journals A fixed point theorem in H-space and related results

1990 ◽  
Vol 42 (1) ◽  
pp. 133-140 ◽  
Author(s):  
E. Tarafdar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Minimax Inequalities ◽  
The Fixed Point Theorem

The equivalence of a fixed point theorem and the Fan-Knaster-Kuratowski-Mazurkiewicz theorem in H-space has been established. The fixed point theorem is then applied to obtain a theorem on sets with H-convex sections, and also results on minimax inequalities.

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.

On a Fixed Point Theorem of Ky Fan

2002 ◽  
Vol 18 (2) ◽  
pp. 363-374 ◽  
Author(s):  
Francesco S. De Blasi ◽  
Pando Gr. Georgiev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Ky Fan

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 On some fixed point theorems

1989 ◽  
Vol 12 (1) ◽  
pp. 61-64 ◽  
Author(s):  
D. Roux ◽  
S. P. Singh
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Space Setting ◽  
Ky Fan

In this paper we prove a fixed point theorem for inward mappings uing a well-known result of Ky Fan type in Hilbert space setting.

scholarly journals A System of Generalized Variational-Hemivariational Inequalities with Set-Valued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhi-bin Liu ◽  
Jian-hong Gou ◽  
Yi-bin Xiao ◽  
Xue-song Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Directional Derivatives ◽  
Hemivariational Inequalities ◽  
Kkm Theorem ◽  
Special Cases ◽  
Generalized Directional Derivatives ◽  
Set Valued Mappings

By using surjectivity theorem of pseudomonotone and coercive operators rather than the KKM theorem and fixed point theorem used in recent literatures, we obtain some conditions under which a system of generalized variational-hemivariational inequalities concerning set-valued mappings, which includes as special cases many problems of hemivariational inequalities studied in recent literatures, is solvable. As an application, we prove an existence theorem of solutions for a system of generalized variational-hemivariational inequalities involving integrals of Clarke's generalized directional derivatives.

scholarly journals A Class of Fan-Browder Type Fixed-Point Theorem and Its Applications in Topological Space

2010 ◽  
Vol 2010 ◽  
pp. 1-9
Author(s):  
Yi-An Chen ◽  
Yi-Ping Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Topological Space ◽  
Point Theorem ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Topological Spaces ◽  
Related Literature ◽  
The Fixed Point Theorem

A fixed-point theorem is proved under noncompact setting of general topological spaces. By applying the fixed-point theorem, several new existence theorems of solutions for equilibrium problems are proved under noncompact setting of topological spaces. These theorems improve and generalize the corresponding results in related literature.

An RS-KKM Theorem in FC-Metric Spaces with the Application to Fixed Points

2013 ◽  
Vol 838-841 ◽  
pp. 2215-2218
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Maximal Element ◽  
Metric Spaces ◽  
Recent Literature ◽  
Kkm Theorem ◽  
Kkm Mappings ◽  
Section Theorem ◽  
Element Theorem ◽  
Ky Fan

In this paper, RS-KKM mappings are introduced and an RS-KKM theorem is established in noncompact complete FC-metric spaces. As applications, a Ky Fan section theorem, a maximal element theorem and a Fan-Browder type fixed point theorem are obtained in noncompact complete FC-metric spaces. These results unify, improve and generalize some known results in recent literature.

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