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Shehu Y.,African University of Science and Technology
Journal of Global Optimization | Year: 2012

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solution of generalized mixed equilibrium problem and the set of solutions of the variational inequality problem for a co-coercive mapping in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. Furthermore, new convergence results are deduced and finally we apply our results to solving optimization problems and present other applications. © 2011 Springer Science+Business Media, LLC. Source


Shehu Y.,African University of Science and Technology
Computers and Mathematics with Applications | Year: 2012

The purpose of this paper is to construct a new iterative scheme by the hybrid method and prove a strong convergence theorem for the approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a common solution to infinite systems of equilibrium and variational inequality problems in a uniformly smooth and strictly convex real Banach space with KadecKlee property using the properties of a generalized f-projection operator. Using this result, we give some applications. Our results extend many known recent results in the literature. © 2012 Published by Elsevier Ltd. Source


Shehu Y.,African University of Science and Technology
Mathematical and Computer Modelling | Year: 2011

The purpose of this paper is to introduce a hybrid algorithm for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings and the set of solutions of a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space which also has Kadec-Klee property using the properties of generalized f-projection operator. Our results extend important recent results. © 2011 Elsevier Ltd. Source


Shehu Y.,African University of Science and Technology
Mathematical and Computer Modelling | Year: 2011

In this paper, we construct a new iterative scheme by hybrid method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Furthermore, using our iterative scheme, we prove strong convergence theorem to a common element of the set of fixed point of a weak relatively nonexpansive mapping, set of solutions to a variational inequality problem and the set of common solutions to a system of generalized mixed equilibrium problems. Finally, we give applications of our results in a Banach space. Our results extend many important recent results in the literature. © 2011 Elsevier Ltd. Source


Shehu Y.,African University of Science and Technology
Journal of Global Optimization | Year: 2011

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of common fixed points of a finite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent results. © 2010 Springer Science+Business Media, LLC. Source

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