New three-step iteration process and fixed point approximation in Banach spaces
محورهای موضوعی : Fixed point theory
K. Ullah
1
(Department of Mathematics, International Islamic University H-10, 44000- Islamabad, Pakistan)
M. Arshad
2
(Department of Mathematics, International Islamic University H-10, 44000- Islamabad, Pakistan)
کلید واژه: Banach space, Suzuki generalized nonexpansive mapping, Iteration process, weak convergence, strong convergence, contraction mapping,
چکیده مقاله :
In this paper we propose a new iteration process, called the $K^{\ast }$ iteration process, for approximation of fixedpoints. We show that our iteration process is faster than the existing well-known iteration processes using numerical examples. Stability of the $K^{\ast}$ iteration process is also discussed. Finally we prove some weak and strong convergence theorems for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results are the extension, improvement and generalization of many well-known results in the literature of iterations infixed point theory.
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