On Mixed Equilibrium Problems in Hadamard Spaces
The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-con...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/3210649 |
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| Summary: | The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature. |
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| ISSN: | 2314-4629 2314-4785 |