New iteration process for approximating fixed points in Banach spaces
محورهای موضوعی : Fixed point theory
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
کلید واژه: fixed point, Iteration process, Suzuki generalized nonexpansive mappings, uniformly convex Banach space,
چکیده مقاله :
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.
[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.
