On asymptotically strict pseudocontractions and equilibrium problems

Asymptotically Strict Pseudocontractions

and Applied Analysis 3 3 A mapping G : H → H is said to be semicompact if, for any bounded sequence {xn} ⊂ H with limn→∞‖xn −Gxn‖ 0, there exists a subsequence {xni} ⊂ {xn} such that xni converges strongly to a point x ∗ ∈ H. Now, we give one example of the γ, {kn} -asymptotically strict pseudocontraction mapping. Example 2.3. Let B be the unit ball in a Hilbert space l2, and define a mapping T...

Weak convergence of algorithms for asymptotically strict pseudocontractions in the intermediate sense and equilibrium problems

*Correspondence: [email protected] 2Department of Mathematics Education, Kyungnam University, Masan, 631-701, Korea Full list of author information is available at the end of the article Abstract In this paper, equilibrium problems and fixed-point problems based on an iterative method are investigated. It is proved that the sequence generated in the purposed iterative process weakly conve...

Strong convergence theorems for system of equilibrium problems and asymptotically strict pseudocontractions in the intermediate sense

* Correspondence: [email protected] College of Science, Civil Aviation University of China, Tianjin 300300, PR China Abstract Let {Si}i=1 be N uniformly continuous asymptotically li-strict pseudocontractions in the intermediate sense defined on a nonempty closed convex subset C of a real Hilbert space H. Consider the problem of finding a common element of the fixed point set of these mappings ...

Viscosity-Projection Method for a Family of General Equilibrium Problems and Asymptotically Strict Pseudocontractions in the Intermediate Sense

In this paper, a Meir-Keeler contraction is introduced to propose a viscosity-projection approximation method for finding a common element of the set of solutions of a family of general equilibrium problems and the set of fixed points of asymptotically strict pseudocontractions in the intermediate sense. Strong convergence of the viscosity iterative sequences is obtained under some suitable con...

Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces