scholarly journals On θ-generalized demimetric mappings and monotone operators in Hadamard spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 95-111 ◽  
Author(s):  
Grace N. Ogwo ◽  
Chinedu Izuchukwu ◽  
Kazeem O. Aremu ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Monotone Operators ◽  
Finite Family ◽  
Hadamard Space ◽  
Proximal Point ◽  
Main Interest ◽  
Minimization Problems ◽  
Convex Feasibility ◽  
Convex Minimization Problems

AbstractOur main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.

A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space

2020 ◽  
pp. 2150058
Author(s):  
K. O. Aremu ◽  
C. Izuchukwu ◽  
A. A. Mebawondu ◽  
O. T. Mewomo
Keyword(s):  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Feasibility Problem ◽  
Point Problem ◽  
Hadamard Space ◽  
Proximal Point ◽  
Common Solution

In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping recently introduced by Phuengrattana [Appl. Gen. Topol. 18 (2017) 117–129]. We establish a strong convergence result of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a generalized asymptotically nonspreading and nonexpansive mappings, which is also a unique solution of some variational inequality problems in an Hadamard space. We apply our result to solve convex feasibility problem and to approximate a common solution of a finite family of minimization problems in an Hadamard space.

scholarly journals On the proximal point algorithm and demimetric mappings in CAT(0) spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 277-294 ◽  
Author(s):  
Kazeem O. Aremu ◽  
Chinedu Izuchukwu ◽  
Godwin C. Ugwunnadi ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Proximal Point Algorithm ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Proximal Point ◽  
Numerical Example ◽  
Common Solution ◽  
Minimization Problems

Abstract In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore,we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

scholarly journals A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sabiya Khatoon ◽  
Watcharaporn Cholamjiak ◽  
Izhar Uddin
Keyword(s):  
Computational Result ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Common Element ◽  
Proximal Point ◽  
Minimization Problems ◽  
Numerical Result ◽  
Convex Minimization Problems ◽  
The Common

AbstractIn this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of $\operatorname{CAT}(0)$ CAT ( 0 ) spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration.

scholarly journals A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
N. Kaewyong ◽  
L. Kittiratanawasin ◽  
C. Pukdeboon ◽  
K. Sitthithakerngkiet
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Splitting Method ◽  
Zero Point ◽  
Monotone Operators ◽  
Multivalued Mappings ◽  
Strong Convergence Theorem ◽  
Proximal Algorithm ◽  
Proximal Point

We modify a hybrid method and a proximal point algorithm to iteratively find a zero point of the sum of two monotone operators and fixed point of nonspreading multivalued mappings in a Hilbert space by using the technique of forward-backward splitting method. The strong convergence theorem is established and the illustrative numerical example is presented on this work. The results of this paper extend and improve some well-known results in the literature.

Approximating the minimum-norm fixed point of pseudocontractive mappings

2015 ◽  
Vol 08 (02) ◽  
pp. 1550036
Author(s):  
H. Zegeye ◽  
O. A. Daman
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Convergence Result ◽  
Monotone Mappings ◽  
Minimum Norm ◽  
Nonlinear Operators ◽  
Linear Inverse Problems ◽  
Minimization Problems ◽  
Pseudocontractive Mappings ◽  
Convex Minimization Problems

We introduce an iterative process which converges strongly to the minimum-norm fixed point of Lipschitzian pseudocontractive mapping. As a consequence, convergence result to the minimum-norm zero of monotone mappings is proved. In addition, applications to convexly constrained linear inverse problems and convex minimization problems are included. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

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