TY - JOUR AU - Jaiboon, Chaichana AU - Plubtieng, Somyot AU - Katchang, Phayap PY - 2018 TI - The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces JO - Journal of Nonlinear Sciences and Applications SP - 746--761 VL - 11 IS - 6 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.06.02 DO - 10.22436/jnsa.011.06.02 ID - Jaiboon2018 ER - TY - JOUR TI - Strong convergence of Mann’s-type iterations for nonexpansive semigroups in general Banach spaces AU - S. Atsushiba AU - W. Takahashi JO - Nonlinear Anal. PY - 2005 DA - 2005// VL - 61 ID - Atsushiba2005 ER - TY - JOUR TI - Some geometric properties related to the fixed point theory for nonexpansive mappings AU - J.-P. Gossez AU - E. Lami Dozo JO - Pacific J. Math. PY - 1972 DA - 1972// VL - 40 ID - Gossez1972 ER - TY - JOUR TI - An iterative method for variational inequality problems AU - W.-B. Guan JO - J. Inequal. Appl. PY - 2013 DA - 2013// VL - 2013 ID - Guan 2013 ER - TY - JOUR TI - The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces AU - Y. Ke AU - C. Ma JO - Fixed Point Theory Appl. PY - 2015 DA - 2015// VL - 2015 ID - Ke2015 ER - TY - BOOK TI - Amenability and fixed point property for semigroup of nonexpansive mapping AU - A. T.-M. Lau PB - Fixed point theory Appl. (Marseille, (1989)), Pitman Res. Notes Math. Ser. Longman Sci. Tech. PY - 1991 DA - 1991// CY - Harlow ID - Lau1991 ER - TY - JOUR TI - Fixed point properties of semigroups of non-expansive mappings AU - A. T.-M. Lau AU - Y. Zhang JO - J. Funct. Anal. PY - 2008 DA - 2008// VL - 254 ID - Lau2008 ER - TY - JOUR TI - On characterizations of Meir-Keeler contractive maps AU - L.-C. Lim JO - Nonlinear Anal. PY - 2001 DA - 2001// VL - 46 ID - Lim 2001 ER - TY - JOUR TI - 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 AU - P. Sunthrayuth AU - P. Kumam JO - Math. Comput. Modelling PY - 2013 DA - 2013// VL - 58 ID - Sunthrayuth2013 ER - TY - JOUR TI - Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals AU - T. Suzuki JO - J. Math. Anal. Appl. PY - 2005 DA - 2005// VL - 305 ID - Suzuki 2005 ER - TY - JOUR TI - Moudafi’s viscosity approximations with MeirKeeler contractions AU - T. Suzuki JO - J. Math. Anal. Appl. PY - 2007 DA - 2007// VL - 325 ID - Suzuki2007 ER - TY - JOUR TI - Hybrid method for a class of accretive variational inequalities involving nonexpansive mappings AU - Y. Wang AU - H.-K. Xu JO - J. Inequal. Appl. PY - 2014 DA - 2014// VL - 2014 ID - Wang2014 ER - TY - JOUR TI - Iterative algorithms for nonlinear operators AU - H.-K. Xu JO - J. London Math. Soc. PY - 2002 DA - 2002// VL - 66 ID - Xu2002 ER - TY - JOUR TI - The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces AU - H.-K. Xu AU - M. A. Alghamdi AU - N. Shahzad JO - Fixed Point Theory Appl. PY - 2015 DA - 2015// VL - 2015 ID - Xu2015 ER - TY - JOUR TI - Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces AU - Q. Yan AU - G. Cai AU - P. Luo JO - J. Nonlinear Sci. Appl. PY - 2016 DA - 2016// VL - 9 ID - Yan2016 ER -