Document Type: Research Paper


1 Department of Mathematics‎, ‎Cooch Behar College‎, ‎Cooch Behar‎, ‎West Bengal‎, ‎Pin Code 736101‎, ‎India

2 Department of Mathematics‎, ‎Raiganj University‎, ‎Raiganj‎, ‎Pin Code 733134‎, ‎India


‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our results‎. ‎Our results improves many known results of the existing literature‎.


Main Subjects

[1] M. Abbas, T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesn. 66 (2) (2014), 223-234.

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

[3] V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, 2007.

[4] Lj. Ciric, A. Rafiq, S. Radenovi´ c, M. Rajovi´ c, J. S. Ume, On Mann implicit iterations for strongly accreative and strongly pseudo-contractive mappings, App. Math. Comput. 198 (2008), 128-137.

[5] D. Dukic, Lj. Paunovic, S. Radenovic, Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces, Kragujevac J. Math. 35 (3) (2011), 399-410.

[6] F. Gursoy, V. Karakaya, A Picard S-hybrid type iteration method for solving differential equation with retarded argument, arXiv:1403.2546v2, 2014.

[7] A. M. Harder, Fixed Point Theory and Stability Results for Fixed Point Iteration Procedures, Ph.D Thesis, University of Missouri-Rolla, Missouri, 1987.

[8] N. Hussain, K. Ullah, M. Arshad, Fixed point approximation for Suzuki generalized nonexpansive mappings via new iteration process, J. Nonlinear Convex Anal. 19 (8) (2018), 1383-1393.

[9] S. Ishikawa, Fixed points by a new iteration method, Proc. Am. Math. Soc. 44 (3) (1974), 147-150.

[10] V. Karakaya, N. E. H. Bouzara, K. Dogan, Y. Atalan, On different results for a new two-step iteration method under weak-contraction mapping in Banach spaces, arXiv:1507.00200v1.

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

[12] M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (1) (2000), 217-229.

[13] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc. 43 (1) (1991), 153-159.

[14] T. Suzuki, Fixed point theorems and convergence theorems for some generalized non-expansive mappings, J. Math. Anal. 340 (2) (2008), 1088-1095.

[15] B. S. Thakur, D. Thakur, M. Postolache, A new iteration scheme for approximating fixed points of nonexpansive mappings, Filomat. 30 (10) (2016), 2711-2720.

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

[17] K. Ullah, M. Arshad, New iteration process and numerical reckoning fixed point in Banach spaces, U.P.B. Sci. Bull. (Series A). 79 (4) (2017), 113-122.

[18] K. Ullah, M. Arshad, New three-step iteration process and fixed point approximation in Banach spaces, J. Linear. Topological. Algebra. (7) (2) (2018), 87-100.

[19] K. Ullah, M. Arshad, Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat. 32 (1) (2018), 187-196.

[20] K. Ullah, M. Arshad, On different results for new three step iteration process in Banach spaces, SpringerPlus. (2016), 2016:1616.

[21] K. Ullah, K. Iqbal, M. Arshad, Some convergence results using K iteration process in CAT(0) spaces, Fixed Point Theory Appl. (2018), 2018:11.

[22] X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Am. Math. Soc. 113 (1991), 727-731.