Study of equilibrium problem in Hadamard manifolds by extending some concepts of nonlinear analysis
| Autor: | Ali Farajzadeh, S. M. Vaezpour, R. Rahimi |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
021103 operations research Algebra and Number Theory Hadamard three-circle theorem Mathematics::Operator Algebras Applied Mathematics Hadamard three-lines theorem 010102 general mathematics Mathematical analysis 0211 other engineering and technologies Existence theorem Hadamard manifold 02 engineering and technology 01 natural sciences Hadamard's inequality Computational Mathematics Hadamard transform Geometry and Topology 0101 mathematics Finite intersection property Analysis Maximal element Mathematics |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 112:1521-1537 |
| ISSN: | 1579-1505 1578-7303 |
| DOI: | 10.1007/s13398-017-0441-4 |
| Popis: | In this paper, we attempt to define a new KKM map for nonself maps in the setting of Hadamard manifolds, which is then utilized to state the finite intersection property in this framework. Subsequently, this property is used to develop the Fan-KKM theorem for nonself maps on Hadamard manifolds. Moreover, a new definition of upper semicontinuouty and a generalization of the closedness of a set are also proposed. Inspired by this extension, we establish a new existence theorem of a solution to the equilibrium problem for nonself maps on Hadamard Manifolds. As an application of our KKM theorem, we obtain an existence result of maximal elements for nonself set valued mappings in Hadamard manifold frameworks. Finally, for the sake of clarity, a number of examples are presented throughout the paper and our results are compared with the results of some other papers. |
| Databáze: | OpenAIRE |
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