numerical Reckoning Fixed Points for Berinde Mappings via a Faster iteration Process

Osman Alagoz, Birol Gunduz, Sezgin Akbulut

DOI Number
First page
Last page


In this work we prove that $M$-iteration process converges strongly faster than $S$-iteration and Picard-$S$ iteration processes. Moreover $M-$ iteration process is faster than $S_n$ iteration process with a sufficient condition for weak contractive mapping defined on a normed linear space. We also give two numerical reckoning examples to support our main theorem. For approximating fixed points, all codes were written in MAPLE \textcircled{c}2018 All rights reserved.


Iteration process, fixed point, weak contractive mapping, normed linear space.


faster iteration, Berinde mapping, rate of convergence

Full Text:



V. Berinde, Picard iteration converges faster than Mann iteraiton for a class of quasicontractive operators, Fixed Point Theory and Applications 2 (2001) 97-105.

F. Gursoy, V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, aeXiv:1403.254v2 (2014)

Picard, E., (1890). ”M´emoire sur la th´eorie des ´equations aux d´eriv´ees partielles et la m´ethodedes approximations successives”, Journal de Math´ematiques pures et appliqu´ees, 6:145-210.

Noor, M.A. 2000. New approximation schemes for general variational inequalities. Journal of

Mathematical Analysis and Applications 251: 217-229.

Phuengrattana, W. Suantai, S. 2011. On the rate of convergence of Mann, Ishikawa, Noor

and SP-iterations for continuous functions on an arbitrary interval. Journal of Computational and Applied Mathematics 235: 3006-3014.

Chugh, R., Kumar, V. Kumar, S. 2012. Strong Convergence of a new three step iterative

scheme in Banach spaces. American Journal of Computational Mathematics 2: 345-357.

Karahan, I. Ozdemir, M. 2013. A general iterative method for approximation of fixed points

and their applications. Advances in Fixed Point Theory 3(3).

Sahu, D. R. Petrusel, A. 2011. Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces. NonlinearAnalysis: Theory, Methods Applications

(17): 6012-6023.

Thianwan, S. 2009. Common fixed points of new iterations for two asymptotically nonexpansive

nonself-mappings in a Banach space. Journal of Computational and Applied Mathematics

: 688-695.

W. Sintunavarat and A. Pitea, On a new iteraiton scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis, J. Nonlinear Sci. Appl., 9 (2016), 2553-2562

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

W.R. Mann, Mean value methods in iteraiton, Proc. Am. Math. Soc. 4 (1953) 506-510

S. Ishikawa, Fixed points by a new iteraiton method, Proc. Am. Math. Soc. 44 (1974) 147-150.

R. P. Agarwal, D. O'Regan, D.R. Sahu, iteraitve construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. 8 (1), (2007) 61-79

T. Zamfirescu, Fixed point theorems in metric spaces, Arch.i 23 (1972), 292-298.1

M. Abbas, T. Nazir, A new faster iteraiton process applied to constrained minimization and feasibility problems, Mathematiu{c}ki Vesnik, 66 (2) (2014) 223-234

K. Ullah and M. Arshad, Numarical Reckoning Fixed Points for Suzuki's Generalized Nonexpansive Mappings via Iteration Process, Filomat, 32:1 (2018), 187-196.



  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)