Quasi-Intersection Problems and Fixed Point Theorems Concerning Separately Scalar Weakly l.s.c and u.s.c Mappings

Abstract

In this paper, we first prove a new result on quasi-variational inequality problems; then, we use it to show the existence of solutions to quasi-intersection problems. In particular, we establish several results on the existence of solutions to generalized quasi-equilibrium problems and fixed point problems concerning separately scalar weakly lower and upper semi-continuous mappings. The results in this paper generalize some well-known existence theorems from the literature.

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Acknowledgments

The second author of the paper is a member of the project “Joint study in Analysis and Geometry” conducted at the International Center for Research and Training in Mathematics, Institute of Mathematics, VAST, ICRTM01-2019.05; he would like to thank other members of the project for useful discussions. This work was supported by the Vietnam Academy of Science and Technologies under the code NVCC1.14/19-19.

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Correspondence to Truong Thi Thuy Duong.

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Dedicated to Hoang Tuy on the occasion of his 90th birthday

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Duong, T.T.T., Tan, N.X. Quasi-Intersection Problems and Fixed Point Theorems Concerning Separately Scalar Weakly l.s.c and u.s.c Mappings. Acta Math Vietnam 45, 311–328 (2020). https://doi.org/10.1007/s40306-019-00344-3

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Keywords

  • Quasi-intersection problems
  • Separately scalar weakly upper and separately scalar weakly lower semi-continuous mappings
  • Fixed point theorems
  • Quasi-equilibrium problems

Mathematics Subject Classification (2010)

  • 49J27
  • 49J53
  • 91B50
  • 90C48