Strong convergence theorems for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces

The Convergence Theorems for Common Fixed Points of Uniformly L-lipschitzian Asymptotically Φ-pseudocontractive Mappings

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...

Strong convergence for total asymptotically pseudocontractive semigroups in Banach spaces

*Correspondence: [email protected] Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China Abstract In this article, the demiclosedness principle for total asymptotically pseudocontractions in Banach spaces is established. The strong convergence to a common fixed point of total asymptotically pseudocontractive semigroups in Banach spaces is established based on the demiclosednes...

Convergence theorems for uniformly quasi-Lipschitzian mappings

On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces

Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the cond...

Strong Convergence Theorems for Lipschitzian Demicontraction Semigroups in Banach Spaces

The purpose of this paper is to introduce and study the strong convergence problem of the explicit iteration process for a Lipschitzian and demicontraction semigroups in arbitrary Banach spaces. The main results presented in this paper not only extend and improve some recent results announced by many authors, but also give an affirmative answer for the open questions raised by Suzuki 2003 and X...