The iterative solution for a class of monotone operator equations

1999 ◽  
Vol 4 (2) ◽  
pp. 143-145 ◽  
Author(s):  
Xiao Jin-sheng ◽  
Lei Jin-gan
Keyword(s):  
Monotone Operator ◽  
Iterative Solution ◽  
Operator Equations

PRP-like algorithm for monotone operator equations

2021 ◽  
Author(s):  
Auwal Bala Abubakar ◽  
Poom Kumam ◽  
Hassan Mohammad ◽  
Abdulkarim Hassan Ibrahim
Keyword(s):  
Monotone Operator ◽  
Operator Equations

scholarly journals Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hua Su
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Iterative Solution ◽  
Order Method ◽  
Operator Equations ◽  
Abstract Operator ◽  
Uniqueness Of A Solution

In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.

A derivative-free iterative method for nonlinear ill-posed equations with monotone operators

2017 ◽  
Vol 25 (5) ◽  
pp. 543-551 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Monotone Operator ◽  
Regularization Parameter ◽  
A Priori ◽  
Monotone Operators ◽  
Adaptive Procedure ◽  
Operator Equations ◽  
Derivative Free ◽  
Ill Posed

AbstractRecently, Semenova [12] considered a derivative free iterative method for nonlinear ill-posed operator equations with a monotone operator. In this paper, a modified form of Semenova’s method is considered providing simple convergence analysis under more realistic nonlinearity assumptions. The paper also provides a stopping rule for the iteration based on an a priori choice of the regularization parameter and also under the adaptive procedure considered by Pereverzev and Schock [11].

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