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Juan Enrique Martínez-Legaz, Cornel Pintea, Closed convex sets that are both Motzkin decomposable and generalized Minkowski sets

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DOI: 10.23952/jnva.8.2024.4.06

Volume 8, Issue 4, 1 August 2024, Pages 571-579

 

Abstract. We consider and characterize closed convex subsets of the Euclidean space which are simultaneously Motzkin decomposable and generalized Minkowski or, shortly, MdgM sets. We also prove the existence of suitably defined fixed points for, possibly multivalued, functions defined on MdgM sets along with the existence of classical fixed points for some single valued self functions of MdgM sets. The first mentioned type of existence results are based on Kakutani fixed point theorem, and the second type are based both on the Brouwer fixed point theorem and the Banach contraction principle.

 

How to Cite this Article:
J.E. Martínez-Legaz, C. Pintea, Closed convex sets that are both Motzkin decomposable and generalized Minkowski sets, J. Nonlinear Var. Anal. 8 (2024), 571-579.