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Inclusion and intersection theorems with applications in equilibrium theory in g-convex spaces

Balaj, Mircea
; 
O'Regan, Donal
Identifiers
http://hdl.handle.net/10379/10329
https://doi.org/10.13025/28496
Repository DOI
10.4134/jkms.2010.47.5.1017
Publication Date
2010-09-01
Keywords
g-convex space, the better admissible class, fixed point, equilibrium problems, kkm type theorems, fixed-point theorems, fc-spaces, coincidence theorems, vectorial equilibria, existence, inequalities
Type
Article
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Citation
Balaj, Mircea; O'Regan, Donal (2010). Inclusion and intersection theorems with applications in equilibrium theory in g-convex spaces. Journal of the Korean Mathematical Society 47 (5), 1017-1029
Abstract
In this paper we obtain a very general theorem of rho-compatibility for three multivalued mappings, one of them from the class B. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation rho on 2(Z) and three mappings P : X (sic) Z, Q : Y (sic) Z and T is an element of B(Y, X) satisfying a set of conditions we can find ((x) over tilde, (y) over tilde) is an element of X x Y such that (x) over tilde is an element of T((y) over tilde) and P((x) over tilde)rho Q((y) over tilde). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.
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Publisher
The Korean Mathematical Society
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)