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Abstract: Our purpose in this paper is to construct a new iterative scheme by the hybrid method and prove the strong convergence theorem using our new iterative scheme for approximation of a common fixed point of a countable family of uniformly quasi--asymptotically 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 the Kadec–Klee property using the properties of the generalized -projection operator. Our results extend many known recent results in the literature. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Using our results, we obtain the mean ergodic theorem for nonexpansive mappings in Hilbert spaces. Our results extend many recent important results. [Copyright &y& Elsevier]

Abstract: 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 -projection operator. Our results extend important recent results. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to construct a new iterative scheme by hybrid methods to approximate a common element of the common fixed points set of a finite family of -asymptotically nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. Our results extend many known recent results in the literature. [Copyright &y& Elsevier]

Abstract: 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 solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Furthermore, using our new iterative scheme, we prove strong convergence theorems which extend many recent important results. Finally, we apply our results to solve an optimization problem in a real Hilbert space. [Copyright &y& Elsevier]