A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space

[EN] The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.Izuchukwu, C.; Aremu, KO.; Mebawondu, AA.; Mewomo, OT. (2019). A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space. Applied General Topology. 20(1):193-210. https://doi.org/10.4995/agt.2019.10635SWORD193210201K. O. Aremu, C. Izuchukwu, G. C. Ugwunnadi and O. T. Mewomo, On the proximal point algorithm and demimetric mappings in CAT(0) spaces, Demonstr. Math. 51 (2018), 277-294. https://doi.org/10.1515/dema-2018-0022M. 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In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces. We also analyse asymptotic behaviour of the sequence generated by Halpern-type proximal point algorithm and extend it to approximate a common solution of a finite family of minimization problems in the setting of complete p-uniformly convex metric spaces. Furthermore, numerical experiments of our algorithms in comparison with other algorithms are given to show the applicability of our results.http://link.springer.com/journal/110752019-11-19hj2018Mathematics and Applied Mathematic

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