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3 2014

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Fixed point theorems for a semigroup of total asymptotically nonexpansive mappings in uniformly convex Banach spaces

Suantai S., Phuengrattana W.

Opuscula Mathematica

2014

Vol. 34, no. 1

183--197

In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.

Strong convergence theorems of one-step iterative scheme for a countable family of multivalued mappings in a Banach space

Bunyawat A., Suantai S.

Fasciculi Mathematici

2014

Nr 53

31--38

In this paper, we introduce a new one-step iterative scheme for finding a common fixed point of a countable family of multivalued mappings in a real uniformly convex Banach space. By using the best approximation operators, a necessary and sufficient condition for strong convergence of the proposed method is given. Moreover, we establish some strong convergence theorems of the proposed iterative scheme under some control conditions

Viscosity approximation methods for nonexpansive multi-valued nonself mappings and equilibrium problems

Cholamjiak P., Cholamjiak W., Suantai S.

Demonstratio Mathematica

2014

Vol. 47, nr 2

382--395

In this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.