scholarly journals Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mathew Aibinu ◽  
Surendra Thakur ◽  
Sibusiso Moyo
Keyword(s):  
Fixed Point ◽  
Nonlinear Operator ◽  
Monotone Mappings ◽  
Operator Equations ◽  
Fredholm Type ◽  
Nonlinear Operator Equations ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings ◽  
Implicit Iterative Algorithm ◽  
Strictly Pseudocontractive Mappings

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ-strictly pseudocontractive mappings, solution of α-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type.

scholarly journals Fixed Point Theorems on Nonlinear Binary Operator Equations with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Baomin Qiao
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Order Theory ◽  
Iteration Theory ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Monotone Iteration ◽  
Binary Operator

The existence and uniqueness for solution of systems of some binary nonlinear operator equations are discussed by using cone and partial order theory and monotone iteration theory. Furthermore, error estimates for iterative sequences and some corresponding results are obtained. Finally, the applications of our results are given.

scholarly journals A New Iterative Method for the Set of Solutions of Equilibrium Problems and of Operator Equations with Inverse-Strongly Monotone Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jong Kyu Kim ◽  
Nguyen Buong ◽  
Jae Yull Sim
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Finite Family ◽  
Common Element ◽  
Monotone Mappings ◽  
Operator Equations ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings ◽  
New Iterative Method

The purpose of the paper is to present a new iteration method for finding a common element for the set of solutions of equilibrium problems and of operator equations with a finite family ofλi-inverse-strongly monotone mappings in Hilbert spaces.

scholarly journals An Iterative Method with Norm Convergence for a Class of Generalized Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Haixia Zhang ◽  
Fenghui Wang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Monotone Mappings ◽  
Norm Convergence ◽  
Inverse Strongly Monotone ◽  
Generalized Equilibrium ◽  
Strongly Monotone Mappings

Recently, Takahashi and Takahashi proposed an iterative algorithm for solving a problem for finding common solutions of generalized equilibrium problems governed by inverse strongly monotone mappings and of fixed point problems for nonexpansive mappings. In this paper, we provide a result that allows for the removal of one condition ensuring the strong convergence of the algorithm.

scholarly journals Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

1986 ◽  
Vol 9 (3) ◽  
pp. 583-587
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

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