On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme
Abstract
The aim of this paper is to obtain results of the strong convergence, rate of convergence and data dependence for a new three step iterative scheme using contraction mappings and to give examples for the rate of convergence and data dependence results. After these numerical approachs, it can be seen that the new iterative scheme has a better rate of convergence with respect to the other iterative schemes in the literature. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.
Keywords
References
- [1] R. P. Agarwal, D. O Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. Vol:8, No:1 (2007), 61-79.
- [2] S. Ishikawa, Fixed Point By a New Iteration Method, Proc. Amer. Math. Soc. Vol:44 (1974), 147-150.
- [3] W. R. Mann, Mean Value Methods in Iteration, Proc. Amer. Math. Soc., Vol:4 (1953), 506-510.
- [4] M.A Noor, New Approximation Schemes for General Variational Inequalities, J. Math. Anal. Appl. Vol:251, (2000), 217-229.
- [5] V. Karakaya, Y. Atalan, K. Dogan, NEH. Bouzara, Some Fixed Point Results for a new three steps iteration process in Banach spaces, Fixed Point Theory, Vol:18 No:2 (2017) 625-640.
- [6] R.Chugh, V. Kumar, S. Kumar, Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces, Amer. J. Comp. Math. Vol:2, No:04 (2012), 345-357.
- [7] E. Picard, Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl, Vol:6 No:4 (1890), 145-210.
- [8] K. Dogan, Daha Hızlı Mann Sabit Nokta Yinelemesi U¨ zerine Bir C¸ alıs¸ma, Afyon Kocatepe U¨ niversitesi Fen ve Mu¨hendislik Bilimleri Dergisi, Vol:18, No:3 (2018), 852-860.
Details
Primary Language
English
Subjects
Engineering
Journal Section
Research Article
Authors
Yunus Atalan
*
0000-0002-5912-7087
Türkiye
Publication Date
April 15, 2019
Submission Date
November 20, 2018
Acceptance Date
March 6, 2019
Published in Issue
Year 2019 Volume: 7 Number: 1
