scholarly journals Integral Operators of Mixed Type of Nonlinear Integral Equation

2018 ◽  
Vol 27 (4) ◽  
pp. 117-127
Author(s):  
Lamyaa H. Saadoon
Keyword(s):  
Integral Equation ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Integral Operators

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 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 Localized boundary-domain integral equation formulation for mixed type problems

2010 ◽  
Vol 17 (3) ◽  
pp. 469-494 ◽  
Author(s):  
Otar Chkadua ◽  
Sergey E. Mikhailov ◽  
David Natroshvili
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Variable Coefficient ◽  
Mixed Type ◽  
Mixed Boundary ◽  
Integral Operators ◽  
Mixed Boundary Value Problem ◽  
Domain Integral ◽  
Integral Equation Formulation

Abstract Some modifed direct localized boundary-domain integral equations (LBDIEs) systems associated with the mixed boundary value problem (BVP) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the corresponding localized boundary-domain integral operators in appropriately chosen function spaces.

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.

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