scholarly journals A HYBRID PROJECTION METHOD FOR COMMON ZERO OF MONOTONE OPERATORS IN HILBERT SPACES

2017 ◽  
Vol 32 (2) ◽  
pp. 447-456 ◽  
Author(s):  
Minh Tuyen Truong
Keyword(s):  
Projection Method ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Common Zero ◽  
Hybrid Projection Method

scholarly journals On a System of Nonlinear Variational Inclusions withHh,η-Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Zeqing Liu ◽  
Jeong Sheok Ume ◽  
Shin Min Kang
Keyword(s):  
Hilbert Spaces ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
Iterative Approximation

This paper is concerned mainly with the existence and iterative approximation of solutions for a system of nonlinear variational inclusions involving the stronglyHh,η-monotone operators in Hilbert spaces. The results presented in this paper extend, improve, and unify many known results in the literature.

Generalized relaxed inertial method with regularization for solving split feasibility problems in real Hilbert spaces

2021 ◽  
pp. 2250106
Author(s):  
A. A. Mebawondu ◽  
L. O. Jolaoso ◽  
H. A. Abass ◽  
O. K. Narain
Keyword(s):  
Hilbert Spaces ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Split Feasibility Problem ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Inertial Method ◽  
Split Feasibility

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the aforementioned problems without using the conventional two cases approach. In addition, we apply our convergence results to the classical variational inequality and equilibrium problems, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

scholarly journals Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1836
Author(s):  
Yaqian Jiang ◽  
Rudong Chen ◽  
Luoyi Shi
Keyword(s):  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Linear Convergence ◽  
Monotone Operators ◽  
Null Point ◽  
Point Problem ◽  
Bounded Linear ◽  
Zero Points

The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results.

scholarly journals Zeros of Nonlinear Monotone Operators in Hilbert Space*

1978 ◽  
Vol 21 (2) ◽  
pp. 213-219 ◽  
Author(s):  
R. Schöneberg
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Russian Mathematician ◽  
Image Position

Around 1960, the Russian mathematician Kachurovski [1] introduced the notion of monotone operators in Hilbert spaces: Let E be a Hilbert space and X ⊂ E. An operator T:X→E is said to be monotone, iff.

scholarly journals A new system of variational inclusions with (H, η)-monotone operators in hilbert spaces

2005 ◽  
Vol 49 (2-3) ◽  
pp. 365-374 ◽  
Author(s):  
Ya-Ping Fang ◽  
Nan-Jing Huang ◽  
H.B. Thompson
Keyword(s):  
Hilbert Spaces ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
New System

Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems

2019 ◽  
Vol 26 (1) ◽  
pp. 63-78
Author(s):  
Kaleem Raza Kazmi ◽  
Rehan Ali
Keyword(s):  
Banach Space ◽  
Projection Method ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Solution Set ◽  
Common Element ◽  
Monotone Mappings ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Hybrid Projection Method

Abstract The aim of this paper is to consider a generalized mixed variational-like inequality problem and prove a Minty-type lemma for its related auxiliary problems in a real Banach space. We prove the existence of a solution of these auxiliary problems. Further, we prove some properties of a solution set of generalized mixed variational-like inequality problems. Furthermore, we use a hybrid projection method to find a common element of a solution set of a system of unrelated generalized mixed variational-like inequality problems for generalized relaxed α-monotone mappings and the set of fixed points of a common fixed point problem for a family of generalized asymptotically quasi-ϕ-nonexpansive mappings in a reflexive, uniformly smooth and strictly convex Banach space.

On the hybrid projection method for fixed point and equilibrium problems

Top ◽  
2011 ◽  
Vol 21 (2) ◽  
pp. 341-354
Author(s):  
Xiaolong Qin ◽  
Sun Young Cho ◽  
Shin Min Kang ◽  
Feng Gu
Keyword(s):  
Fixed Point ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Hybrid Projection Method
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