Research Article

Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces

Volume: 46 Number: 3 June 1, 2017
EN

Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces

Abstract

In this paper, we simplify the iterative scheme introduced by Fukhar-ud-din and Berinde [Iterative Methods for the Class of Quasi-Contractive Type Operators and Comparison of their Rate of Convergence in Convex Metric Spaces, Filomat 30 (1), 223230, 2016] and study convergence and data dependency of the new proposed scheme of a quasi-contractive operator on a hyperbolic space. It is shown that our results provide better convergence rate.

Keywords

References

  1. Abbas, M., Khan, S. H. Some $\Delta-$convergence theorems in $CAT(0)$ spaces, Hacet. J. Math. Stat. 40 (4), 563569, 2011.
  2. Agarwal, R. P., O' Regan, D. and Sahu, D. R. Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8 (1), 6179, 2007.
  3. Berinde, V. Iterative approximation of fixed points (Springer-Verlag, Berlin, 2007).
  4. Bridson, M. and Haeiger, A. Metric spaces of non-positive curvature (Springer-Verlag, Berlin, 1999).
  5. Chugh, R. and Kumar, V. Data dependence of Noor and SP iterative schemes when dealing with quasi-contractive operators, Int. J. Comput. Appl. 40 (15), 4146, 2011.
  6. Dhompongsa, S. and Panyanak, B. On $\Delta-$convergence theorems in $CAT(0)$ spaces, Comput. Math. Appl. 56 (10), 25722579, 2008.
  7. Fukhar-ud-din H. One step iterative scheme for a pair of nonexpansive mappings in a convex metric space, Hacet. J. Math. Stat. 44 (5), 10231031, 2015.
  8. Fukhar-ud-din, H. and Berinde, V. Iterative Methods for the Class of Quasi-Contractive Type Operators and Comparsion of their Rate of Convergence in Convex Metric Spaces, Filomat 30 (1), 223230, 2016.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

June 1, 2017

Submission Date

April 29, 2016

Acceptance Date

July 26, 2016

Published in Issue

Year 2017 Volume: 46 Number: 3

APA
Gursoy, F., Khan, A. R., & Fukhar-ud-din, H. (2017). Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics, 46(3), 373-388. https://izlik.org/JA85UZ58YF
AMA
1.Gursoy F, Khan AR, Fukhar-ud-din H. Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics. 2017;46(3):373-388. https://izlik.org/JA85UZ58YF
Chicago
Gursoy, Faik, Abdul Rahim Khan, and Hafiz Fukhar-ud-din. 2017. “Convergence and Data Dependence Results for Quasi-Contractive Type Operators in Hyperbolic Spaces”. Hacettepe Journal of Mathematics and Statistics 46 (3): 373-88. https://izlik.org/JA85UZ58YF.
EndNote
Gursoy F, Khan AR, Fukhar-ud-din H (June 1, 2017) Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics 46 3 373–388.
IEEE
[1]F. Gursoy, A. R. Khan, and H. Fukhar-ud-din, “Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, pp. 373–388, June 2017, [Online]. Available: https://izlik.org/JA85UZ58YF
ISNAD
Gursoy, Faik - Khan, Abdul Rahim - Fukhar-ud-din, Hafiz. “Convergence and Data Dependence Results for Quasi-Contractive Type Operators in Hyperbolic Spaces”. Hacettepe Journal of Mathematics and Statistics 46/3 (June 1, 2017): 373-388. https://izlik.org/JA85UZ58YF.
JAMA
1.Gursoy F, Khan AR, Fukhar-ud-din H. Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics. 2017;46:373–388.
MLA
Gursoy, Faik, et al. “Convergence and Data Dependence Results for Quasi-Contractive Type Operators in Hyperbolic Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, June 2017, pp. 373-88, https://izlik.org/JA85UZ58YF.
Vancouver
1.Faik Gursoy, Abdul Rahim Khan, Hafiz Fukhar-ud-din. Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics [Internet]. 2017 Jun. 1;46(3):373-88. Available from: https://izlik.org/JA85UZ58YF