Research Article

On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme

Volume: 7 Number: 1 April 15, 2019
EN

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. [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. [2] S. Ishikawa, Fixed Point By a New Iteration Method, Proc. Amer. Math. Soc. Vol:44 (1974), 147-150.
  3. [3] W. R. Mann, Mean Value Methods in Iteration, Proc. Amer. Math. Soc., Vol:4 (1953), 506-510.
  4. [4] M.A Noor, New Approximation Schemes for General Variational Inequalities, J. Math. Anal. Appl. Vol:251, (2000), 217-229.
  5. [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. [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. [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. [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

Publication Date

April 15, 2019

Submission Date

November 20, 2018

Acceptance Date

March 6, 2019

Published in Issue

Year 2019 Volume: 7 Number: 1

APA
Atalan, Y. (2019). On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp Journal of Mathematics, 7(1), 97-106. https://izlik.org/JA52BY62NF
AMA
1.Atalan Y. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp J. Math. 2019;7(1):97-106. https://izlik.org/JA52BY62NF
Chicago
Atalan, Yunus. 2019. “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”. Konuralp Journal of Mathematics 7 (1): 97-106. https://izlik.org/JA52BY62NF.
EndNote
Atalan Y (April 1, 2019) On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp Journal of Mathematics 7 1 97–106.
IEEE
[1]Y. Atalan, “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”, Konuralp J. Math., vol. 7, no. 1, pp. 97–106, Apr. 2019, [Online]. Available: https://izlik.org/JA52BY62NF
ISNAD
Atalan, Yunus. “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”. Konuralp Journal of Mathematics 7/1 (April 1, 2019): 97-106. https://izlik.org/JA52BY62NF.
JAMA
1.Atalan Y. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp J. Math. 2019;7:97–106.
MLA
Atalan, Yunus. “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”. Konuralp Journal of Mathematics, vol. 7, no. 1, Apr. 2019, pp. 97-106, https://izlik.org/JA52BY62NF.
Vancouver
1.Yunus Atalan. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp J. Math. [Internet]. 2019 Apr. 1;7(1):97-106. Available from: https://izlik.org/JA52BY62NF
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.