Taiwanese Journal of Mathematics

Fixed Point Theorems on Product Topological Semilattice Spaces, Generalized Abstract Economies and Systems of Generalized Vector Quasi-equilibrium Problems

Suliman Al-Homidan and Qamrul Hasan Ansari

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Abstract

In this paper, we establish fixed point theorems for a family of multivalued maps defined on the product space of topological semilattice spaces. By using our fixed point theorems, we derive a result on the nonempty intersection of sets without convex structure and equilibrium existence theorems for generalized abstract economies with two constraint correspondences. We present some special cases of our results which generalize several known results in the literature. We consider systems of generalized vector quasi-equilibrium problems and their special cases. As an application of our equilibrium existence theorems, we establish some existence results for solutions of systems of generalized vector quasi-equilibrium problems and their special cases. The results of this paper improve and extend several results in the literature.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 307-330.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406176

Digital Object Identifier
doi:10.11650/twjm/1500406176

Mathematical Reviews number (MathSciNet)
MR2780286

Zentralblatt MATH identifier
1237.47060

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 90C29: Multi-objective and goal programming 49J40: Variational methods including variational inequalities [See also 47J20] 91A10: Noncooperative games
Secondary: 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 91B52: Special types of equilibria 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

Keywords
fixed point theorems generalized abstract economies intersection theorems systems of generalized vector quasi-equilibrium problems topological semilattice spaces

Citation

Al-Homidan, Suliman; Ansari, Qamrul Hasan. Fixed Point Theorems on Product Topological Semilattice Spaces, Generalized Abstract Economies and Systems of Generalized Vector Quasi-equilibrium Problems. Taiwanese J. Math. 15 (2011), no. 1, 307--330. doi:10.11650/twjm/1500406176. https://projecteuclid.org/euclid.twjm/1500406176


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