A Newton-like method for the numerical solution of nonlinear Fredholm-type operator equations

2012 ◽  
Vol 218 (20) ◽  
pp. 10129-10148 ◽  
Author(s):  
L. Kohaupt
Keyword(s):  
Numerical Solution ◽  
Type Operator ◽  
Operator Equations ◽  
Fredholm Type

Solvability of mixed type operator equations

2007 ◽  
Vol 190 (2) ◽  
pp. 1344-1352 ◽  
Author(s):  
Ibrahim Abouelfarag Ibrahim
Keyword(s):  
Mixed Type ◽  
Type Operator ◽  
Operator Equations

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 A two step newton type iteration for ill-posed Hammerstein type operator equations in Hilbert scales

2014 ◽  
Vol 26 (1) ◽  
pp. 91-116
Author(s):  
Monnanda Erappa Shobha ◽  
Santhosh George ◽  
M. Kunhanandan
Keyword(s):  
Type Operator ◽  
Operator Equations ◽  
Ill Posed
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