Iterative method to find approximate solution of system of integral equations via generalized Meir–Keeler condensing operator

2021 ◽  
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
Nipen Saikia ◽  
Nihar Kumar Mahato
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Integral Equations ◽  
System Of Integral Equations ◽  
Condensing Operator

scholarly journals Coupled fixed points and α-dense curves

2016 ◽  
Vol 32 (3) ◽  
pp. 323-330
Author(s):  
G. GARCIA ◽  
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonexpansive Mappings ◽  
Volterra Type ◽  
System Of Integral Equations ◽  
Compactness Condition ◽  
New Iterative Method ◽  
Coupled Fixed Points

We present a new iterative method, based on the so called α-dense curves, to approximate coupled fixed points of nonexpansive mappings. Compactness condition on the mapping or its domain of definition is necessary. As application, we construct a sequence which converges to a solution of certain system of integral equations of Volterra type.

scholarly journals Approximate solutionn of a nonllinear system of integral equations using modified Newton-Kantorovich method

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Z.K. Eshkuvatov ◽  
A. Akhmedov ◽  
N.M.A. Nik Long ◽  
O. Shafiq
Keyword(s):  
Approximate Solution ◽  
Integral Operator ◽  
Integral Equations ◽  
Iteration Method ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Kantorovich Method ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Nonlinear Integral Operator

Modified Newton-Kantorovich method is developed to obtain an approximate solution for a system of nonlinear integral equations. The system of nonlinear integral equations is reduced to find the roots of nonlinear integral operator. This nonlinear integral operator is solved by the modified Newton-Kantorovich method with initial conditions and this procedure is continued by iteration method to find the unknown functions. The existence and uniqueness of the solutions of the system are also proven.

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

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