A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings

In this paper, we propose a new iterative algorithm to approximate fixed point of Suzuki's generalized nonexpansive mappings. We establish some weak and strong convergence theorems in a uniformly convex Banach space. We also provide examples to illustrate the convergence behavior of the proposed algorithm.

[1]  Yunan Cui,et al.  Iterative Approximations for Generalized Multivalued Mappings in Banach Spaces , 2012 .

[2]  Withun Phuengrattana.  Approximating fixed points of Suzuki-generalized nonexpansive mappings , 2011 .

[3]  Sompong Dhompongsa,et al.  Edelstein's method and fixed point theorems for some generalized nonexpansive mappings , 2009 .

[4]  Mujahid Abbas,et al.  A new faster iteration process applied to constrained minimization and feasibility problems , 2014 .

[5]  Tomonari Suzuki,et al.  FIXED POINT THEOREMS AND CONVERGENCE THEOREMS FOR SOME GENERALIZED NONEXPANSIVE MAPPINGS , 2008 .

[6]  J. Schu,et al.  Weak and strong convergence to fixed points of asymptotically nonexpansive mappings , 1991, Bulletin of the Australian Mathematical Society.

[7]  Enrique Llorens-Fuster,et al.  Fixed point theory for a class of generalized nonexpansive mappings , 2011 .

[8]  W. Petryshyn.  Construction of fixed points of demicompact mappings in Hilbert space , 1966 .

[9]  W. R. Mann,et al.  Mean value methods in iteration , 1953 .

[10]  S. Ishikawa.  Fixed points by a new iteration method , 1974 .

[11]  W. G. Dotson,et al.  Approximating fixed points of nonexpansive mappings , 1974 .

[12]  B. Rhoades,et al.  Some fixed point iteration procedures , 1991 .

[13]  B. Rhoades,et al.  Fixed point iterations using infinite matrices , 1974 .

[14]  Z. Opial.  Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[15]  M. Noor.  New approximation schemes for general variational inequalities , 2000 .

[16]  Mohammad Eslamian,et al.  Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces , 2010 .