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-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 Halperntype 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.
Other information
Published in: Journal of Mathematics
License: http://creativecommons.org/licenses/by/4.0
See article on publisher's website: http://dx.doi.org/10.1155/2019/3210649
Funding
Open Access funding provided by the Qatar National Library.
History
Language
- English
Publisher
HindawiPublication Year
- 2019
License statement
This Item is licensed under the Creative Commons Attribution 4.0 International License.Institution affiliated with
- Qatar University
- College of Arts and Sciences - QU