Research Article

Some Strong and Δ - Convergence Results in Hyperbolic Spaces

by  Preety Malik
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 170 - Issue 9
Published: Jul 2017
Authors: Preety Malik
10.5120/ijca2017914906
PDF

Preety Malik . Some Strong and Δ - Convergence Results in Hyperbolic Spaces. International Journal of Computer Applications. 170, 9 (Jul 2017), 11-16. DOI=10.5120/ijca2017914906

                        @article{ 10.5120/ijca2017914906,
                        author  = { Preety Malik },
                        title   = { Some Strong and Δ - Convergence Results in Hyperbolic Spaces },
                        journal = { International Journal of Computer Applications },
                        year    = { 2017 },
                        volume  = { 170 },
                        number  = { 9 },
                        pages   = { 11-16 },
                        doi     = { 10.5120/ijca2017914906 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2017
                        %A Preety Malik
                        %T Some Strong and Δ - Convergence Results in Hyperbolic Spaces%T 
                        %J International Journal of Computer Applications
                        %V 170
                        %N 9
                        %P 11-16
                        %R 10.5120/ijca2017914906
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this paper is to prove some strong and Δ-convergence results for modified Khan et. al. iterative procedures using total asymptotically quasi-nonexpansive mappings in Hyperbolic spaces. The results are the generalization and extension of some results of Agarwal et. al. [12], Cho and Abbas [17], Basarir and Sahin [10], Chang et. al. [18], Agarwal et. al. [12], Aggarwal and Chugh [11], Khan et. al. [15], Sahin and Basarir [1].

References
  • Sahin, A. and Basarir, M. On the strong convergence of a modified S-iteration process for asymptotically quasi-nonexpansive mappings in a CAT(0) space, Fixed Point Theory and Applications, vol. 2013, no 12, (2013) , doi:10.1186/1687-1812-2013-12.
  • Khan, A. R., Fukhar-ud-din, H. and Khan, M. A. An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl., vol.54, (2012), 12 pages.
  • Fukhar-ud-din, H. and Khan, S. H. 2007 Convergence of iterates with errors of asymptotically quasi nonexpansive mappings and applications, J. Math. Anal. Appl., vol. 328, (2007), 821-829.
  • Senter, H. F. and Dotson, W. G. Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., vol. 44, (1974), 375–380.
  • Schu, J. Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., vol. 43, (1991), 153-159.
  • Tan, K. K. and Xu, H. K. Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., vol. 122, (1994), 733-739.
  • Goebel, K. and Kirk, W. A. A fixed point theorem for asymptotically nonexpansive mappings, proc. Amer. Math. Soc., vol. 35, no. 1, (1972), 171-174.
  • Qihou, L. Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl., vol. 259, (2001), 1-7.
  • Leustean, L. Nonexpansive iterations in uniformly convex W-hyperbolic spaces. In: Leizarowitz, A, Mordukhovich, BS, Shafrir, I, Zaslavski, A (eds.) Nonlinear Analysis and Optimization I: Nonlinear Analysis. Contemp. Math., vol. 513, pp. 193-209. Am. Math. Soc., Providence (2010)
  • Basarir, M. and Sahin A., On the strong and Δ-convergence for total asymptotically nonexpansive mappings 0n a CAT(0) space, Carpathian Math. Publ., vol. 5, no 2, (2013), 170-179.
  • Aggarwal, M. and Chugh, R. Strong and -convergence of Khan et. al. iterative procedure in CAT(0) spaces, Differential Geometry, Functional Analysis and Applications, Narosa Publishing House, New Delhi, 2015, 143-155.
  • Agarwal, R. P., O'Regan, D. and Sahu D. R., Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J.Nonlinear Convex Anal., vol. 8, no. 1, (2007), 61-79.
  • Chugh, R. Preety and  Aggarwal, M. Some convergence results for modified S-iterative scheme in Hyperbolic spaces, International Journal of Computer Applications, 80 (6), 2013, 20-23.
  • Dhompongsa, S. and Panyanak, B. On Δ-convergence theorems in CAT(0) spaces, Comput. Math. Appl., vol 56, (2008), 2572-2579.
  • Khan S. H. and Jong Kyu Kim, Common fixed points of two nonexpansive mappings by a modified faster iteration scheme, Bull. Korean Math. Soc., vol. 47, no. 5, (2010), 973-985.
  • Khan, S. H. and Abbas, M. Strong and Δ-convergence of some iterative schemes in CAT(0) spaces, Computers and Mathematics with Applications, vol. 61, (2011), 109-116.
  • Khan, S. H., Cho, Y. J. and Abbas, M. Convergence to common fixed points by a modified iteration process, J. Appl math. Comput. Vol. 35, (2011), 607-616.
  • Chang, S. S., Wang, L., Joseph Lee, H. W. and Chan, C. K. Demiclosed principle and Δ-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) Spaces, Appl. Math. Comput., vol. 219, (2012) , 2611-2617.
  • Diaz, S. B. and Metcalf, F. B. On the structure of the set of sequential limit points of successive approximations, Bull. Amer. Math. Soc., vol. 73, (1967), 516-519.
  • Lim, T.C. Remarks on some fixed point theorems, Proc. Amer. Math. Soc., vol. 60, (1976), 179–182.
  • Shimizu, T. and Takahashi, W. Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal., vol. 8, (1996), 197-203.
  • Kuczumow, T. An almost convergence and its applications, Ann. Univ. Mariae Curie-Sklodowska, Sect. A., vol. 32, (1978),79-88.
  • Kohlenbach, U.  Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. Soc., vol. 357(2005), 89-128.
  • Petryshyn, W. V. and Williamson, T. E. Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. math. Anal. Appl., vol. 43, (1973), 459-497.
  • Takahashi, W.  A convexity in metric spaces and nonexpansive mapping, Kodai Math. Sem. Rep., vol. 22, (1970), 142-149.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Hyperbolic spaces Δ-convergence strong convergence total asymptotically quasi nonexpansive mappings common fixed point Iterative procedures.

Powered by PhDFocusTM