CONVERGENCE OF S-ITERATIVE METHOD TO A SOLUTION OF FREDHOLM INTEGRAL EQUATION AND DATA DEPENDENCY

Yunus Atalan, Faik Gursoy, Abdul Rahim Khan

DOI Number
https://doi.org/10.22190/FUMI190116051A
First page
685
Last page
694

Abstract


The convergence of normal S-iterative method to solution of a nonlinear
Fredholm integral equation with modied argument is established. The corresponding
data dependence result has also been proved. An example in support of the established results is included in our analysis.


Keywords

Fredholm equation; data dependency; Fixed-point theorem

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References


Y. Atalan and V. Karakaya: Iterative solution of functional Volterra-Fredholm integral equation with deviating argument. J. Nonlinear Convex Anal. 18 (2017), 675-684.

V. Berinde: Existence and approximation of solutions of some first order iterative differential equations. Miskolc Math. Notes. 11 (2010), 13-26.

V. Berinde: Picard iteration converges faster than the Mann iteration in the class of quasi-contractive operators. Fixed Point Theory A. 2004 (2004), 97-105.

M. Dobritoiu: System of integral equations with modified argument. Carpathian J. Math. 24 (2008), 26-36.

M. Dobritoiu and A. M. Dobritoiu: An approximating algorithm for the solution of an integral equation from epidemics. Ann. Univ. Ferrara, 56 (2010), 237-248.

M. Dobritoiu: A class of nonlinear integral equations. Transylvanian Journal of Mathematics and Mechanics, 4 (2012), 117-123.

F. Gursoy: Applications of normal S-iterative method to a nonlinear integral equation. The Scientific World Journal, 2014 (2014), 1-5.

E. Hacioglu, F. Gursoy, S. Maldar, Y. Atalan, and G. V. Milovanovic: Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning. Appl. Numer. Math., 167, (2021), 143-172.

N. Hussain, V. Kumar and M. A. Kutbi: On rate of convergence of Jungck-Type

iterative schemes. Abstr. Appl. Anal. 2013 (2013), 1-15.

S. Ishikawa: Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44

(1974), 147-150.

S. M. Kang, A. Rafiq and S. Lee: Strong convergence of an implicit S-iterative process for lipschitzian hemicontractive mappings. Abstr. Appl. Anal. 2012 (2012), 1-7.

S. H. Khan: A Picard-Mann hybrid iterative process. Fixed Point Theory A., 2013 (2013),1-10.

S. H. Khan: Fixed points of contractive-like operators by a faster iterative process. WASET International Journal of Mathematical, Computational Science and Engineering. 7 (2013), 57-59.

A. R. Khan, V. Kumar and N. Hussain: Analytical and numerical treatment of Jungck-type iterative schemes. Appl. Math. Comput. 231 (2014), 521-535.

A. R. Khan, F. Gursoy and V. Karakaya: Jungck-Khan iterative scheme and higher convergence rate. Int. J. Comput. Math. 93 (2016), 2092-2105.

S. A. Khuri and A. Sayfy: Variational iteration method: Green's functions and fixed point iterations perspective. Appl. Math. Lett., 32 (2014), 24-34.

S. A. Khuri and A. Sayfy: A novel fixed point scheme: Proper setting of variational

iteration method for BVPs. Appl. Math. Lett., 48 (2015), 75-84.

V. Kumar, A. Latif, A. Rafiq and N. Hussain: S-iteration process for quasi-contractive mappings. J. Inequal. Appl. 2013 (2013), 1-15.

M. Lauran: Existence results for some differential equations with deviating argument. Filomat, 25 (2011), 21-31.

S. Maldar, F. Gursoy, Y. Atalan and M. Abbas: On a three-step iteration process for multivalued Reich-Suzuki type $alpha$-nonexpansive and contractive mappings. J.

Appl. Math. Comput., (2021), 1-21.

W. R. Mann: Mean value methods in iteration. Proc. Amer.Math. Soc. 4 (1953), 506-510.

E. Picard: Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives. J. Math. Pure. Appl. 6 (1890), 145-210.

D. R. Sahu: Applications of S iteration process to constrained minimization problems and split feasibility problems. Fixed Point Theory, 12 (2011), 187-204.

D. R. Sahu and A. Petrusel: Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces. Nonlinear Anal. Theor. 74 (2011), 6012-6023.

S. M. Soltuz and T. Grosan: Data dependence for Ishikawa iteration when dealing with contractive like operators. Fixed Point Theory Appl. 2008 (2008), 1-7.




DOI: https://doi.org/10.22190/FUMI190116051A

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