A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space-Reference-Cited by-同舟云学术

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

Published:2019-04-01 Issue:1 Volume:20 Page:193
ISSN:1989-4147
Container-title:Applied General Topology
language:
Short-container-title:Appl. Gen. Topol.

Author:

Izuchukwu C.,Aremu K. O.,Mebawondu A. A.,Mewomo O. T.

Abstract

<p>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.</p>

Publisher

Universitat Politecnica de Valencia

Subject

Geometry and Topology

Reference39 articles.

1. K. 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-2018-0022

2. M. Bacák, The proximal point algorithm in metric spaces, Israel J. Math. 194 (2013), 689-701. https://doi.org/10.1007/s11856-012-0091-3

3. M. Bacák and S. Riech, The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces, J. Fixed Point Theory Appl. 16 (2014), 189-202. https://doi.org/10.1007/s11784-014-0202-3

4. I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Alexandrov spaces, Geom. Dedicata 133 (2008), 195-218. https://doi.org/10.1007/s10711-008-9243-3

5. M. Bianchi and S. Schaible, Generalized monotone bifunctions and equilibrium problems, J. Optim Theory Appl. 90 (1996), 31-43. https://doi.org/10.1007/BF02192244

Cited by 38 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Strong Convergence Results for Variational Inequality and Equilibrium Problem in Hadamard Spaces;Kragujevac Journal of Mathematics;2023-12

2. A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces;Fixed Point Theory and Algorithms for Sciences and Engineering;2023-04-17

3. A modified viscosity iterative method for implicit midpoint rule for optimization and fixed point problems in CAT(0) spaces;Afrika Matematika;2023-03-20

4. Iterative algorithms for a finite family of equilibrium problems and fixed point problem in an Hadamard space;Fixed Point Theory;2023-02-01

5. A modified Halpern-proximal point method for approximating solutions of mixed equilibrium and fixed point problems in Hadamard spaces;Arabian Journal of Mathematics;2022-06-14