%0 Journal Article %T The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces %A Jaiboon, Chaichana %A Plubtieng, Somyot %A Katchang, Phayap %J Journal of Nonlinear Sciences and Applications %D 2018 %V 11 %N 6 %@ ISSN 2008-1901 %F Jaiboon2018 %X In this research, we focus on a common fixed point problem of a nonexpansive semigroup with the generalized viscosity methods for implicit iterative algorithms. Our main objective is to construct the new strong convergence theorems under certain appropriate conditions in uniformly convex and uniformly smooth Banach spaces. Specifically, the main results make a contribution to the implicit midpoint theorems. The findings for theorems in Hilbert spaces and the other forms of a nonexpansive semigroup can be used in several practical purposes. Finally, a numerical example in 3 dimensions is provided to support our main results. %9 journal article %R 10.22436/jnsa.011.06.02 %U http://dx.doi.org/10.22436/jnsa.011.06.02 %P 746--761 %0 Journal Article %T Strong convergence of Mann’s-type iterations for nonexpansive semigroups in general Banach spaces %A S. Atsushiba %A W. Takahashi %J Nonlinear Anal. %D 2005 %V 61 %F Atsushiba2005 %0 Journal Article %T Some geometric properties related to the fixed point theory for nonexpansive mappings %A J.-P. Gossez %A E. Lami Dozo %J Pacific J. Math. %D 1972 %V 40 %F Gossez1972 %0 Journal Article %T An iterative method for variational inequality problems %A W.-B. Guan %J J. Inequal. Appl. %D 2013 %V 2013 %F Guan 2013 %0 Journal Article %T The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces %A Y. Ke %A C. Ma %J Fixed Point Theory Appl. %D 2015 %V 2015 %F Ke2015 %0 Book %T Amenability and fixed point property for semigroup of nonexpansive mapping %A A. T.-M. Lau %D 1991 %I Fixed point theory Appl. (Marseille, (1989)), Pitman Res. Notes Math. Ser. Longman Sci. Tech. %C Harlow %F Lau1991 %0 Journal Article %T Fixed point properties of semigroups of non-expansive mappings %A A. T.-M. Lau %A Y. Zhang %J J. Funct. Anal. %D 2008 %V 254 %F Lau2008 %0 Journal Article %T On characterizations of Meir-Keeler contractive maps %A L.-C. Lim %J Nonlinear Anal. %D 2001 %V 46 %F Lim 2001 %0 Journal Article %T Viscosity approximation methods based on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces %A P. Sunthrayuth %A P. Kumam %J Math. Comput. Modelling %D 2013 %V 58 %F Sunthrayuth2013 %0 Journal Article %T Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals %A T. Suzuki %J J. Math. Anal. Appl. %D 2005 %V 305 %F Suzuki 2005 %0 Journal Article %T Moudafi’s viscosity approximations with MeirKeeler contractions %A T. Suzuki %J J. Math. Anal. Appl. %D 2007 %V 325 %F Suzuki2007 %0 Journal Article %T Hybrid method for a class of accretive variational inequalities involving nonexpansive mappings %A Y. Wang %A H.-K. Xu %J J. Inequal. Appl. %D 2014 %V 2014 %F Wang2014 %0 Journal Article %T Iterative algorithms for nonlinear operators %A H.-K. Xu %J J. London Math. Soc. %D 2002 %V 66 %F Xu2002 %0 Journal Article %T The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces %A H.-K. Xu %A M. A. Alghamdi %A N. Shahzad %J Fixed Point Theory Appl. %D 2015 %V 2015 %F Xu2015 %0 Journal Article %T Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces %A Q. Yan %A G. Cai %A P. Luo %J J. Nonlinear Sci. Appl. %D 2016 %V 9 %F Yan2016