Common fixed points of strict pseudocontractions by iterative algorithms

Some results on fixed points of asymptotically strict quasi-φ-pseudocontractions in the intermediate sense

*Correspondence: [email protected] 2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, China Full list of author information is available at the end of the article Abstract In this paper, a new nonlinear mapping, asymptotically strict quasi-φ-pseudocontraction in the intermediate sense, is introduced. Projection algorithms are considered for ...

Strong convergence theorems for fixed points of asymptotically strict quasi-φ-pseudocontractions

It is known that a uniformly convex Banach space is reflexive and strictly convex. E is said to be smooth provided limt→ ‖x+ty‖–‖x‖ t exists for all x, y ∈UE . It is also said to be uniformly smooth if the limit is attained uniformly for all x, y ∈UE . It is well known that if E* is strictly convex, then J is single valued; if E* is reflexive, and smooth, then J is single valued and demicontin...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

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...