486 research outputs found
A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems
We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature
A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators
The purpose of this paper is to introduce a new iterative scheme for finding a common
element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of
variational inequality problems, the zero point of maximal monotone operators, and the set of two
countable families of quasi-Ï•-nonexpansive mappings in Banach spaces. Moreover, the strong convergence
theorems of this method are established under the suitable conditions of the parameter imposed
on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone
operators and complementarity problems. Our results presented in this paper improve and extend
the recently results by many others
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