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 Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

A general procedure for rational inequalities

2015 ◽  
Vol 08 (01) ◽  
pp. 1550014
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
General Procedure ◽  
General Theorem ◽  
Type Inequality ◽  
Special Cases ◽  
Rational Type

Recently Bhatt, Chaukiyal and Dimri proved a fixed point theorem for a pair of maps satisfying a rational type inequality. It is the purpose of this paper to show that this result, along with a number of others, are all special cases of a general theorem of Sehie Park.

scholarly journals Multiple Positive Symmetric Solutions top-Laplacian Dynamic Equations on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-27
Author(s):  
You-Hui Su ◽  
Can-Yun Huang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Discrete Equations ◽  
Special Cases ◽  
Krasnosel’Skii’S Fixed Point Theorem

This paper makes a study on the existence of positive solution top-Laplacian dynamic equations on time scales𝕋. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

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 Fixed Point Theorems for Set-Valued Mappings under Contractive Condition in Quasi-Metric Spaces

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Mohseni Kolagar ◽  
Y.J. Cho ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Generalized Weak Contraction ◽  
Banach’S Fixed Point Theorem ◽  
Set Valued Mappings ◽  
Weakly Contractive

Abstract In this paper, we introduce the concept of a generalized weak contraction for set-valued mappings defined on quasi-metric spaces. We show the existence of fixed points for generalized weakly contractive set-valued mappings. Indeed, we have a generalization of Nadler’s fixed point theorem and Banach’s fixed point theorem in quasi-metric spaces and, further, investigate the convergence of iterate scheme of the form xn+1 ∈ Fxn with error estimates.

A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings

1991 ◽  
Vol 34 (4) ◽  
pp. 559-562
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence Theorem ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Nonexpansive Semigroups ◽  
Lipschitzian Mappings ◽  
Lipschitzian Semigroup

AbstractAs a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.

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