Comments on the Rate of Convergence between Mann and Ishikawa Iterations Applied to Zamfirescu Operators

On Equivalence between Convergence of Ishikawa––mann and Noor Iterations

In this paper, we prove the equivalence of convergence between the Mann–Ishikawa– Noor and multistep iterations for Φ− strongly pseudocontractive and Φ− strongly accretive type operators in an arbitrary Banach spaces. Results proved in this paper represent an extension and refinement of the previously known results in this area. Mathematics subject classification (2010): 47H09, 47H10, 47H15.

Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps

Let X, d be a complete metric space, and let T be a self-map of X. If T has a unique fixed point, which can be obtained as the limit of the sequence {pn}, where pn Tp0, p0 any point of X, then T is called a Picard operator see, e.g., 1 , and the iteration defined by {pn} is called Picard iteration. One of the most general contractive conditions for which a map T is a Picard operator is that of ...

Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings

The Comparison of the Convergence Speed between Picard, Mann, Krasnoselskij and Ishikawa Iterations in Banach Spaces

Some Convergence Results for the Jungck-mann and the Jungck-ishikawa Iteration Processes in the Class of Generalized Zamfirescu Operators

In this paper, we shall establish some strong convergence results for the recently introduced Jungck-Mann iteration process of Singh et al. [18] and the newly introduced Jungck-Ishikawa iteration process in the class of non-selfmappings in an arbitrary Banach space. Our results are generalizations and extensions of those of Berinde [4], Rhoades [13, 14] as well as some other analogous ones in t...