%0 Journal Article %T A general implicit iteration for finding fixed points of nonexpansive mappings %A Sahu, D. R. %A Kang, Shin Min %A Kumar, Ajeet %A Cho, Sun Young %J Journal of Nonlinear Sciences and Applications %D 2016 %V 9 %N 8 %@ ISSN 2008-1901 %F Sahu2016 %X The aim of the paper is to construct an iterative method for finding the fixed points of nonexpansive mappings. We introduce a general implicit iterative scheme for finding an element of the set of fixed points of a nonexpansive mapping defined on a nonempty closed convex subset of a real Hilbert space. The strong convergence theorem for the proposed iterative scheme is proved under certain assumptions imposed on the sequence of parameters. Our results extend and improve the results given by Ke and Ma [Y. Ke, C. Ma, Fixed Point Theory Appl., 2015 (2015), 21 pages], Xu et al. [H. K. Xu, M. A. Alghamdi, N. Shahzad, Fixed Point Theory Appl., 2015 (2015), 12 pages], and many others. %9 journal article %R 10.22436/jnsa.009.08.01 %U http://dx.doi.org/10.22436/jnsa.009.08.01 %P 5157--5168 %0 Book %T Fixed point theory for Lipschitzian-type mappings with applications, Topological Fixed Point Theory and Its Applications %A R. P. Agarwal %A D. O'Regan %A D. R. Sahu %D 2009 %I Springer %C New York %F Agarwal2009 %0 Journal Article %T The implicit midpoint rule for nonexpansive mappings %A M. A. Alghamdi %A M. A. Alghamdi %A N. Shahzad %A H. K. Xu %J Fixed Point Theory and Appl. %D 2014 %V 2014 %F Alghamdi2014 %0 Journal Article %T A semi-implicit mid-point rule for stiff systems of ordinary differential equations %A G. Bader %A P. Deu hard %J Numer. Math. %D 1983 %V 41 %F Bader1983 %0 Journal Article %T Some iterative methods for finding fixed points and for solving constrained convex minimization problems %A L. C. Ceng %A Q. H. Ansari %A J. C. Yao %J Nonlinear Anal. %D 2011 %V 74 %F Ceng2011 %0 Journal Article %T Recent progress in extrapolation methods for ordinary differential equations %A P. Deu hard %J SIAM Rev. %D 1985 %V 27 %F hard1985 %0 Book %T Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics %A K. Goebel %A W. A. Kirk %D 1990 %I Cambridge University Press %C Cambridge %F Goebel1990 %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 and Appl. %D 2015 %V 2015 %F Ke2015 %0 Journal Article %T Variable KM-like algorithms for fixed point problems and split feasibility problems %A A. Latif %A D. R. Sahu %A Q. H. Ansari %J Fixed Point Theory and Appl. %D 2014 %V 2014 %F Latif2014 %0 Journal Article %T Viscosity approximation methods for fixed-points problems %A A. Moudafi %J J. Math. Anal. Appl. %D 2000 %V 241 %F Moudafi2000 %0 Journal Article %T Implicit midpoint rule to the nonlinear degenerate boundary value problems %A S. Somalia %J Int. J. Comput. Math. %D 2002 %V 79 %F Somalia2002 %0 Journal Article %T Viscosity approximation methods for nonexpansive mappings %A H. K. Xu %J J. Math. Anal. Appl. %D 2004 %V 298 %F Xu2004 %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 and Appl. %D 2015 %V 2015 %F Xu2015 %0 Journal Article %T The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications %A I. Yamada %J Haifa, (2000), Stud. Comput. Math., North-Holland, Amsterdam %D 2001 %V 2001 %F Yamada2001 %0 Journal Article %T Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem %A Y. Yao %A R. P. Agarwal %A M. Postolache %A Y. C. Liou %J Fixed Point Theory and Appl. %D 2014 %V 2014 %F Yao2014 %0 Journal Article %T An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings %A Y. Yao %A Y. C. Liou %A T. L. Lee %A N. C. Wong %J J. Nonlinear Convex Anal. %D 2016 %V 17 %F Yao2016 %0 Journal Article %T Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction %A Y. Yao %A Y. C. Liou %A J. C. Yao %J Fixed Point Theory and Appl. %D 2015 %V 2015 %F Yao2015 %0 Journal Article %T Strong convergence of a self-adaptive method for the split feasibility problem %A Y. Yao %A M. Postolache %A Y. C. Liou %J Fixed Point Theory and Appl. %D 2013 %V 2013 %F Yao2013 %0 Journal Article %T Modified semi-implicit midpoint rule for nonexpansive mappings %A Y. Yao %A N. Shahzad %A Y. C. Liou %J Fixed Point Theory and Appl. %D 2015 %V 2015 %F Yao2015