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.

scholarly journals Sensitivity Analysis for a System of Generalized Nonlinear Mixed Quasi Variational Inclusions withH-Monotone Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Han-Wen Cao
Keyword(s):  
Sensitivity Analysis ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
New System

The existence of the solution for a new system of generalized nonlinear mixed quasi variational inclusions withH-monotone operators is proved by using implicit resolvent technique, and the sensitivity analysis of solution in Hilbert spaces is given. Our results improve and generalize some results of the recent ones.

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

2006 ◽  
Vol 74 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Jianwen Peng ◽  
Jianrong Huang
Keyword(s):  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Iterative Algorithms ◽  
Operator Method ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
Uniqueness Of Solutions ◽  
Special Cases ◽  
The Resolvent Operator ◽  
New System

In this paper, We introduce and study a new system of variational inclusions involving(H, η)-monotone operators in Hilbert spaces. By using the resolvent operator method associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions and the convergence of some new three-step iterative algorithms for this system of variational inclusions and its special cases. The results in this paper extends and improves some results in the literature.

scholarly journals Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving(A,η)-Maximal Relaxed Monotone Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ting-jian Xiong ◽  
Heng-you Lan
Keyword(s):  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
General System ◽  
Monotone Operators ◽  
Inclusion Problem ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Variational Inclusion Problem ◽  
General Systems ◽  
Resolvent Operator Technique

We introduce and study a class of new general systems of set-valued variational inclusions involving(A,η)-maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with(A,η)-maximal relaxed monotone operators, we construct some new iterative algorithms for finding approximation solutions to the general system of set-valued variational inclusion problem and prove the convergence of this algorithm. Our results improve and extend some known results.

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.

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