scholarly journals On Iteration Method to The Solution of More General Volterra Integral Equation in Two Variables and a Data Dependence Result

2021 ◽  
Author(s):  
Samet MALDAR
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Iteration Method ◽  
Data Dependence ◽  
Dependence Result

scholarly journals Applications of Normal S-Iterative Method to a Nonlinear Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Faik Gürsoy
Keyword(s):  
Integral Equation ◽  
Iterative Method ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Data Dependence ◽  
Dependence Result ◽  
Fredholm Functional

It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

scholarly journals Convergence Analysis for a Modified SP Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Fatma Öztürk Çeliker
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Iteration Method ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Dependence Result ◽  
New Iterative Method

We consider a new iterative method due to Kadioglu and Yildirim (2014) for further investigation. We study convergence analysis of this iterative method when applied to class of contraction mappings. Furthermore, we give a data dependence result for fi…xed point of contraction mappings with the help of the new iteration method.

scholarly journals A Picard-S iterative method for approximating fixed point of weak-contraction mappings

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2829-2845 ◽  
Author(s):  
Faik Gürsoy
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Data Dependence ◽  
Weak Contraction ◽  
Dependence Result ◽  
Fredholm Functional

We study the convergence analysis of a Picard-S iterative method for a particular class of weakcontraction mappings and give a data dependence result for fixed points of these mappings. Also, we show that the Picard-S iterative method can be used to approximate the unique solution of mixed type Volterra-Fredholm functional nonlinear integral equation x (t) = F(t, x(t), ?t1,a1... ?tm,am K(t,s,x(s))ds, ?b1,a1...?bm,am H(t,s,x(s))ds). Furthermore, with the help of the Picard-S iterative method, we establish a data dependence result for the solution of integral equation mentioned above.

scholarly journals Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings

2021 ◽  
Vol 34 (4) ◽  
pp. 78-92
Author(s):  
Zena Hussein Maibed ◽  
Ali Qasem Thajil
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Analytic Proof ◽  
Numerical Example ◽  
Contractive Mappings ◽  
Dependence Result

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

On the Volterra integral equation relating creep and relaxation

2008 ◽  
Vol 24 (3) ◽  
pp. 035009 ◽  
Author(s):  
R S Anderssen ◽  
A R Davies ◽  
F R de Hoog
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation
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