502 research outputs found
Strong convergence theorem for strict pseudo-contractions in Hilbert spaces
Abstract In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015:17, 2015), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015:17, 2015) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof
Modified Mann-Halpern Algorithms for Pseudocontractive Mappings
Modified Mann-Halpern algorithms for finding the fixed points of pseudocontractive mappings are presented. Strong convergence theorems are obtained
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
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
Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces
The aim of this paper is to provide some existence theorems of a strict pseudocontraction by the way of a hybrid shrinking projection method, involving some necessary and sufficient conditions. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudocontraction in the framework of real Hilbert spaces. In addition, we also provide certain applications of the main theorems to confirm the existence of the zeros of an inverse strongly monotone operator along with its convergent results
A hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k-strict pseudo-contractions
AbstractIn this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of asymptotically k-strict pseudo-contractions in the setting of real Hilbert spaces. By using our proposed scheme, we get a weak convergence theorem for a finite family of asymptotically k-strict pseudo-contractions and then we modify these algorithm to have strong convergence theorem by using the two hybrid methods in the mathematical programming. Our results improve and extend the recent ones announced by Ceng, et al.’s result [L.C. Ceng, Al-Homidan, Q.H. Ansari and J.C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967–974] Qin, Cho, Kang, and Shang, [X. Qin, Y. J. Cho, S. M. Kang, and M. Shang, A hybrid iterative scheme for asymptotically k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 1902–1911] and other authors
Strong Convergence Theorems for Asymptotically Pseudocontractive Mappings in the Intermediate Sense
In this study, we prove a strong convergence of Noor type scheme for a uniformly L-Lipschitzian and
asymptotically pseudocontractive mappings in the intermediate sense without assuming any form of compactness. Consequently, we also obtain a convergence result for the class of asymptotically strict pseudocontractive mappings in the intermediate sense. Our results are improvements and
extensions of some of the results in literature
-class algorithms for pseudocontractions and -strict pseudocontractions in Hilbert spaces
In this paper we study iterative algorithms for finding a common element of
the set of fixed points of -strict pseudocontractions or finding a
solution of a variational inequality problem for a monotone, Lipschitz
continuous mapping. The last problem being related to finding fixed points of
pseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K.
Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the links
between these know algorithms and the general framework of -class
algorithms studied in [H.H. Bauschke, P.L. Combettes]
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