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Generalized Vector Quasi-Equilibrium Problems

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  • Adela Elisabeta Capătă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400027 Cluj-Napoca, Romania)

Abstract

The aim of this paper is to present new existence results for solutions to a generalized quasi-equilibrium problem with set-valued mappings and moving cones. The key to this approach is a new Browder-type fixed point theorem, which permits working in a new direction with the milder condition of transfer open-valued mapping and considering weaker assumptions on the coving cone. These results are applied to some generalized vector quasi-equilibrium problems with trifunctions and to a vector quasi-equilibrium problem with fuzzy mappings in a fuzzy environment.

Suggested Citation

  • Adela Elisabeta Capătă, 2024. "Generalized Vector Quasi-Equilibrium Problems," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:809-:d:1354174
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    References listed on IDEAS

    as
    1. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    2. Jun-Yi Fu & An-Hua Wan, 2002. "Generalized vector equilibrium problems with set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 259-268, November.
    3. J. Y. Fu, 2006. "Stampacchia Generalized Vector Quasiequilibrium Problems and Vector Saddle Points," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 605-619, March.
    4. L. J. Lin & Z. T. Yu & G. Kassay, 2002. "Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 189-208, July.
    5. Y. Chiang & O. Chadli & J. Yao, 2004. "Generalized Vector Equilibrium Problems with Trifunctions," Journal of Global Optimization, Springer, vol. 30(2), pages 135-154, November.
    6. Truong Duong & Nguyen Tan, 2012. "On the existence of solutions to generalized quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 52(4), pages 711-728, April.
    7. Jun-Yi Fu, 2005. "Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set," Journal of Global Optimization, Springer, vol. 31(1), pages 109-119, January.
    Full references (including those not matched with items on IDEAS)

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