Numerical reckoning fixed points via new faster iteration process




generalized α-nonexpansive mappings, uniformly convex Banach space, iteration process, weak convergence, strong convergence


In this paper, we propose a new iteration process which is faster than the leading S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79], Thakur et al. [App. Math. Comp. 275 (2016), 147-155] and M [Filomat 32, no. 1 (2018), 187-196] iterations for numerical reckoning fixed points. Using new iteration process, some fixed point convergence results for generalized α-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes.


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Author Biographies

Kifayat Ullah, University of Lakki Marwa

Department of Mathematical Science

Junaid Ahmad, International Islamic University

Department of Mathematics

Fida Muhammad Khan, University of Science and Technology

Department of Mathematics


M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik 66, no. 2 (2014) 223-234.

R. P. Agarwal, D. O'Regan and D. S. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications Series: Topological Fixed Point Theory and Its Applications, vol. 6. Springer, New York (2009).

R. P. Agarwal, D. O'Regan and D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79.

K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74 (2011), 4387-4391.

D. Ariza-Ruiz, C. Hermandez Linares, E. Llorens-Fuster and E. Moreno-Galvez, On α-nonexpansive mappings in Banach spaces, Carpath. J. Math. 32 (2016), 13-28.

F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA. 54 (1965), 1041-1044.

D. Gohde, Zum Prinzip der Kontraktiven Abbildung, Math. Nachr. 30 (1965), 251-258.

F. Gursoy and V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarted argument, (2014) arXiv:1403.2546v2.

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

W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Am. Math. Monthly 72 (1965), 1004-1006.

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

M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251, no. 1 (2000), 217-229.

Z. Opial, Weak and strong convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math. Soc. 73 (1967), 591-597.

D. Pant and R. Shukla, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 38, no. 2 (2017), 248-266.

B. E. Rhoades, Some fixed point iteration procedures, Int. J. Math. Math. Sci. 14 (1991), 1-16.

J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159.

T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), 1088-1095.

W. Takahashi, Nonlinear Functional Analysis. Yokohoma Publishers, Yokohoma (2000).

B. S. Thakur, D. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings, App. Math. Comp. 275 (2016), 147-155.

K. Ullah and M. Arshad, Numerical reckoning fixed points for Suzuki's Generalized nonexpansive mappings via new iteration process, Filomat 32, no. 1 (2018), 187-196.

H. H. Wicke and J.M. Worrell, Jr., Open continuous mappings of spaces having bases of countable order, Duke Math. J. 34 (1967), 255-271.




How to Cite

K. Ullah, J. Ahmad, and F. M. Khan, “Numerical reckoning fixed points via new faster iteration process”, Appl. Gen. Topol., vol. 23, no. 1, pp. 213–223, Apr. 2022.