Strong Convergence Theorems for Strictly Asymptotically Pseudocontractive Mappings in Hilbert Spaces

We propose a new (CQ) algorithm for strictly asymptotically pseudo-contractive mappings and obtain a strong convergence theorem for this class ofmappings in the framework of Hilbert spaces.DOI : http://dx.doi.org/10.22342/jims.16.1.29.25-3

On the Convex Feasibility Problem

The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a family depending of the two characteristics: the emptiness and boudedness of the intersection of the family. The case four (the interior of the intersection is empty and the intersection itself is bounded) is unsolved. In this paper we give a (partial) answer for the case four: in the case of two closed convex sets in R3 the regularity property holds.Comment: 14 pages, exposed on 5th International Conference "Actualities and Perspectives on Hardware and Software" - APHS2009, Timisoara, Romani

Equivalence results for implicit Jungck–Kirk type iterations

We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included

On the Equivalence of Stochastic Fixed Point Iterations for Generalized Contractive-Like Operators

We present the equivalence of some stochastic fixed point iterative algorithms by proving the equivalence between the convergence of random implicit Jungck-Kirk-multistep, random implicit Jungck-Kirk-Noor, random implicit Jungck-Kirk-Ishikawa, and random implicit Jungck-Kirk-Mann iterative algorithms for generalized φ-contractive-like random operators defined on separable Banach spaces

Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces

Abstract An iterative algorithm is introduced for the construction of the minimum-norm fixed point of a pseudocontraction on a Hilbert space. The algorithm is proved to be strongly convergent. MSC:47H05, 47H10, 47H17