TY - JOUR AU - Wu, Guangrong AU - Yang, Liping PY - 2016 TI - General iteration scheme for finding the common fixed points of an infinite family of nonexpansive mappings JO - Journal of Nonlinear Sciences and Applications SP - 5720--5732 VL - 9 IS - 11 AB - The purpose of this paper is to suggest and analyze the general viscosity iteration scheme for an infinite family of nonexpansive mappings \(\{T_i\}^\infty_{i=1}\). Additionally, it proves that this iterative scheme converges strongly to a common fixed point of \(\{T_i\}^\infty_{i=1}\) in the framework of reflexive and smooth convex Banach space, which solves some variational inequality. Results proved in this paper improve and generalize recent known results in the literature. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.11.01 DO - 10.22436/jnsa.009.11.01 ID - Wu2016 ER - TY - JOUR TI - Strong convergence theorems of a general iterative process for a finite family of \(\lambda_i\)-strict pseudo-contractions in q-uniformly smooth Banach spaces AU - G. Cai AU - C. S. Hu JO - Comput. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - Cai2010 ER - TY - BOOK TI - Augmented Lagrangian and operator-splitting methods in nonlinear mechanics AU - R. Glowinski AU - P. Le Tallec PB - SIAM Studies in Applied Mathematics PY - 1989 DA - 1989// CY - Philadelphia ID - Glowinski1989 ER - TY - BOOK TI - Topics in Metric Fixed Point Theory, Studies in Advanced Mathematics AU - K. Goebel AU - W. A. Kirk PB - Cambridge University Press PY - 1990 DA - 1990// CY - Cambridge ID - Goebel1990 ER - TY - JOUR TI - A general iterative method for nonexpansive mappings in Hilbert spaces AU - G. Marino AU - H.-K. Xu JO - J. Math. Anal. Appl. PY - 2006 DA - 2006// VL - 318 ID - Marino2006 ER - TY - JOUR TI - New approximation schemes for general variational inequalities AU - M. A. Noor JO - J. Math. Anal. Appl. PY - 2000 DA - 2000// VL - 251 ID - Noor2000 ER - TY - JOUR TI - Strong convergence of Ishikawa iterative method for nonexpansive mappings in Hilbert space AU - M. J. Shang AU - X. L. Qin AU - Y. F. Su JO - J. Math. Inequal. PY - 2007 DA - 2007// VL - 1 ID - Shang2007 ER - TY - JOUR TI - Strong convergence to common fixed points of infinite nonexpansive mappings and applications AU - K. Shimoji AU - W. Takahashi JO - Taiwanese J. Math. PY - 2001 DA - 2001// VL - 5 ID - Shimoji2001 ER - TY - JOUR TI - Strong convergence of Krasnoselskii and Mann's sequences for one-parameter nonexpansive semigroups without Bochner integrals AU - T. Suzuki JO - J. Math. Anal. Appl. PY - 2005 DA - 2005// VL - 305 ID - Suzuki2005 ER - TY - JOUR TI - Viscosity approximation methods for nonexpansive mappings AU - H.-K. Xu JO - J. Math. Anal. Appl. PY - 2004 DA - 2004// VL - 298 ID - Xu2004 ER - TY - JOUR TI - A general iterative method for an infinite family of nonexpansive mappings AU - Y. Yao AU - Y. -C. Liou AU - R. Chen JO - Nonlinear Anal. PY - 2008 DA - 2008// VL - 69 ID - Yao2008 ER - TY - JOUR TI - Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings AU - Y. H. Yao AU - Y.-C. Liou AU - J.-C. Yao JO - Fixed Point Theory and Appl. PY - 2007 DA - 2007// VL - 2007 ID - Yao2007 ER -