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...

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotical...

It is generally conjectured that the Mann iteration converges faster than the Ishikawa iteration for any operator defined on an arbitrary closed convex subset of a Banach space. The recent result of Babu et al [1] shows that this conjecture can be proved for a class of quasi-contractive operators called the Zamfirescu operators[10]. In this paper it is shown that the proof can indeed be general...

Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on theorems zeros strongly quasi- and fixed points hemi-contractions, we extend results to Ishikawa iteration process with er- rors hemi-contractive .

We prove that Mann and Ishikawa iterations are equivalent models dealing with ψ-uniformly pseudocontractive or d-weakly contractive maps without bounded range.

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated methods been introduced. The main aim this paper is to use coordinate affine structure create an algorithm with technique countable family in Hilbert space symmetric directed graph G and prove the weak theor...

We show that the convergences of Jungck, JungckMann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep iteration processes are equivalent for a class of generalized contractivelike operators defined on a Banach space. Our results are generalizations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones in literature.

Michelitsch and Rossler in 1992 have applied seemingly small changes in complex analytic Mandelbrot set function and it makes a remarkable difference in the appearance of obtained fractal images. They named it burning ship as the image looks like a ship is going up in flame. The purpose of this paper is to explore the unidentified geometrical structure of various fractal images after applying i...

in this paper, several $delta$ and strong convergence theorems are established for the ishikawa iterations for nonexpansive mappings in the framework of cat(0) spaces. our results extend and improve the corresponding results