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A System of Generalized Operator Quasi-Equilibrium Problems in Hausdorff Topological Vector Spaces |
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PP: 1133-1140 |
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doi:10.18576/amis/200501
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Author(s) |
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Shivani Sharma,
Gurpreet Kaur,
Abdul Raouf,
Aseel Smerat,
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Abstract |
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| The purpose of this paper is to investigate a system of generalized operator quasi-equilibrium problems (SGOQEP) in Hausdorff topological vector spaces. Such coupled systems arise naturally in two-player operator games and coupled optimisation problems (for instance duopoly-type competition over pricing or production operators, and network-flow or resource-allocation settings with operator-valued capacities or tolls), where each player’s feasible set and payoff depend on the other player’s current position. Under suitable continuity, convexity, and compactness assumptions, existence theorems for solutions are established. Our results generalize and improve various corresponding results for generalized equilibrium and variational inequality problems reported in earlier studies. The problem asks for a pair ( f1◦, f2◦) in a product of operator spaces such that each component satisfies a quasi-equilibrium condition with a constraint map that depends on both components simultaneously. For the compact case, existence is proved using C( f )-quasiconvexity and the Ding–Kim–Tan fixed-point theorem applied to a product auxiliary map. When the operator domains are non-compact, we replace compactness by a φ -condensing assumption on the constraint maps and invoke the maximal-element theorem of Lin, Park and Yu together with an escaping-sequence condition. Earlier results of Raouf–Gupta–Sharma [21], Sharma–Gupta–Raouf [22], Kazmi–Raouf [11, 12] and Kim–Raouf [17] follow as special cases. We also obtain existence of solutions for a system of operator quasi-variational-like inequality problems and derive an operator quasi-saddle point result. |
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