TY - JOUR AU - Klin-eam, Chakkrid AU - Kaskasem, Prondanai AU - Suantai, Suthep PY - 2016 TI - Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces JO - Journal of Nonlinear Sciences and Applications SP - 4963--4975 VL - 9 IS - 7 AB - We introduce a hybrid method for finding a common element of the set of solutions of an equilibrium problem defined on the dual space of a Banach space and the set of common fixed points of a family of generalized nonexpansive mappings and prove strong convergence theorems by using the new hybrid method. Using our main results, we obtain some new strong convergence theorems for finding a solution of an equilibrium problem and a fixed point of a family of generalized nonexpansive mappings in a Banach space. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.07.01 DO - 10.22436/jnsa.009.07.01 ID - Klin-eam2016 ER - TY - JOUR TI - From optimization and variational inequalities to equilibrium problems AU - E. Blum AU - W. Oettli JO - Math. Student PY - 1994 DA - 1994// VL - 63 ID - Blum1994 ER - TY - JOUR TI - Equilibrium programming in Hilbert spaces AU - P. L. Combettes AU - S. A. Hirstoaga JO - J. Nonlinear Convex Anal. PY - 2005 DA - 2005// VL - 6 ID - Combettes2005 ER - TY - JOUR TI - A new projection and convergence theorems for the projections in Banach spaces AU - T. Ibaraki AU - W. Takahashi JO - J. Approx. Theory PY - 2007 DA - 2007// VL - 149 ID - Ibaraki2007 ER - TY - JOUR TI - Strong convergence of a proximal-type algorithm in a Banach space AU - S. Kamimura AU - W. Takahashi JO - SIAM J. Optim. PY - 2002 DA - 2002// VL - 13 ID - Kamimura2002 ER - TY - JOUR TI - Generalized nonexpansive retractions and a proximal-type algorithm in Banach spaces AU - F. Kohsaka AU - W. Takahashi JO - J. Nonlinear Convex Anal. PY - 2007 DA - 2007// VL - 8 ID - Kohsaka2007 ER - TY - JOUR TI - Mean value methods in iteration AU - W. R. Mann JO - Proc. Amer. Math. Soc. PY - 1953 DA - 1953// VL - 4 ID - Mann1953 ER - TY - JOUR TI - Strong convergence to common fixed points of families of nonexpansive mappings in Banach spaces AU - K. Nakajo AU - K. Shimoji AU - W. Takahashi JO - J. Nonlinear Convex Anal. PY - 2007 DA - 2007// VL - 6 ID - Nakajo2007 ER - TY - JOUR TI - Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups AU - K. Nakajo AU - W. Takahashi JO - J. Math. Anal. Appl. PY - 2003 DA - 2003// VL - 279 ID - Nakajo2003 ER - TY - JOUR TI - Weak convergence theorems for nonexpansive mappings in Banach spaces AU - S. Reich JO - J. Math. Anal. Appl. PY - 1979 DA - 1979// VL - 67 ID - Reich1979 ER - TY - BOOK TI - Nonlinear functional analysis, Fixed point theory and its applications AU - W. Takahashi PB - Yokohama Publ. PY - 2000 DA - 2000// CY - Yokohama ID - Takahashi2000 ER - TY - JOUR TI - Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces AU - W. Takahashi AU - Y. Takeuchi AU - R. Kubota JO - J. Math. Anal. Appl. PY - 2008 DA - 2008// VL - 341 ID - Takahashi2008 ER - TY - JOUR TI - A strong convergence theorem for the equilibrium problem with a bifunction defined on the dual space of a Banach space AU - W. Takahashi AU - K. Zembayashi JO - Fixed point theory and its applications, Yokohama Publ., Yokohama PY - 2008 DA - 2008// VL - 197--209 ID - Takahashi2008 ER - TY - JOUR TI - On uniformly convex functions AU - C. Zălinescu JO - J. Math. Anal. Appl. PY - 1983 DA - 1983// VL - 95 ID - Zălinescu1983 ER -