An order theoretic fixed point theorem with application to multivalued variational inequalities with nonsmooth bifunctions

2018 ◽  
Vol 21 (1) ◽  
Author(s):  
Christoph Tietz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Multivalued Variational 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.

scholarly journals ON FINITE-DIMENSIONAL QUASI-VARIATIONAL INEQUALITIES ASSOCIATED WITH DISCONTINUOUS FUNCTIONS

1994 ◽  
Vol 25 (2) ◽  
pp. 143-148
Author(s):  
TETZ C. HUANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Existence Results ◽  
Discontinuous Functions ◽  
Continuity Properties ◽  
Finite Dimensional ◽  
Set Mappings

In this paper, we derive several existence results for quasi-variational inequalities where the functions under consideration need not have any continuity properties. In particular, we obtain a new fixed point theorem for point-to-set mappings which is also a generalization of the famous Kakutani's fixed point the- orem.

scholarly journals A fixed point theorem and its applications to a system of variational inequalities

1999 ◽  
Vol 59 (3) ◽  
pp. 433-442 ◽  
Author(s):  
Qamrul Hasan Ansari ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Existence Theorem ◽  
Point Theorem ◽  
Product Spaces ◽  
Multivalued Maps ◽  
Equilibrium Existence ◽  
Abstract Economy ◽  
System Of Variational Inequalities

In this paper, we first prove a fixed point theorem for a family of multivalued maps defined on product spaces. We then apply our result to prove an equilibrium existence theorem for an abstract economy. We also consider a system of variational inequalities and prove the existence of its solutions by using our fixed point theorem.

scholarly journals Fixed points, intersection theorems, variational inequalities, and equilibrium theorems

2000 ◽  
Vol 24 (2) ◽  
pp. 73-93 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Convex Sets ◽  
Quasi Equilibrium ◽  
Topological Vector Spaces ◽  
Abstract Economies ◽  
General Economic Equilibrium ◽  
Locally Convex

From a fixed point theorem for compact acyclic maps defined on admissible convex sets in the sense of Klee, we first deduce collectively fixed point theorems, intersection theorems for sets with convex sections, and quasi-equilibrium theorems. These quasi-equilibrium theorems are applied to give simple and unified proofs of the known variational inequalities of the Hartman-Stampacchia-Browder type. Moreover, from our new fixed point theorem, we deduce new variational inequalities which can be used to obtain fixed point results for convex-valued maps. Finally, various general economic equilibrium theorems are deduced in the forms of the Nash type, the Tarafdar type, and the Yannelis-Prabhakar type. Our results are stated for not-necessarily locally convex topological vector spaces and for abstract economies with arbitrary number of commodities and agents. Our new results extend a lot of known works with much simpler proofs.

scholarly journals Existence of solutions of inverted variational inequalities

2012 ◽  
Vol 28 (2) ◽  
pp. 271-278
Author(s):  
SZILARD LASZLO ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Generalized Variational Inequalities ◽  
Easy Consequence ◽  
Brouwer’S Fixed Point Theorem ◽  
Brouwer's Fixed Point Theorem

In this paper we introduce two new generalized variational inequalities and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We show by examples, that our results fail outside of this class. Further, we establish a result that may be viewed as a generalization of Minty’s theorem, that is, we show that under some circumstances the set of solutions of these variational inequalities coincide. We also show, the condition that the operators, involved in these variational inequalities, belong to the above mentioned class, is essential in obtaining this result. As application, we show that Brouwer’s fixed point theorem is an easy consequence of our results.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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