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 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 Comparison of two Schemes for Common Fixed Points with an Application

2019 ◽  
Vol 32 (2) ◽  
pp. 81
Author(s):  
Salwa Salman Abed ◽  
Zahra Mahmood Mohamed Hasan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Nonexpansive Maps ◽  
Fredholm Functional

      Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

scholarly journals Fixed point of sum for concave and convex operators with applications

1988 ◽  
Vol 37 (1) ◽  
pp. 81-87
Author(s):  
Li Bingyou
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Theorems ◽  
Linear Spaces ◽  
Existence And Uniqueness Theorems ◽  
Ordered Linear Spaces ◽  
Convex Operators

In this paper we study fixed points of sums of α-concave and (−α)-convex operators in γ-complete partially ordered linear spaces. As an application we obtain existence and uniqueness theorems for solutions of a certain type of nonlinear integral equation.

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 existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

scholarly journals A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Convex Sets ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Modular Space ◽  
Ordinate Axis ◽  
Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

scholarly journals On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
O. Baghani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Operator

The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space . Later on, we give some examples of applications of this type of results.

scholarly journals Fixed Points Of F-Weak Contractions On Complete Metric Spaces

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
D. Wardowski ◽  
N. Van Dung
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Proper Extension

AbstractIn this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature

Sign in / Sign up

Export Citation Format

Share Document