A new iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contractive mappings and its application

In this paper, we introduce a new iterative scheme for finding a common element of the set of a solution of an equilibrium problem and the set of fixed points of finite family strict pseudo-contraction mappings in a real Hilbert space. Some strong convergence theorems are established using the iterative scheme. In the meantime, we successfully apply these Theorems to find a common element of the set of a solution of an equilibrium problem and the set of fixed points of finite family of non-expansive mappings in a real Hilbert space. The results in this paper improve the corresponding ones of [3,6] and references therein

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 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

Iterative algorithms for solutions of nonlinear equations in Banach spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF