Akcije

Mathematica Moravica
kako citirati ovaj članak
podeli ovaj članak

Metrika

  • citati u SCIndeksu: 0
  • citati u CrossRef-u:0
  • citati u Google Scholaru:[]
  • posete u poslednjih 30 dana:3
  • preuzimanja u poslednjih 30 dana:3

Sadržaj

članak: 1 od 1  
2015, vol. 19, br. 1, str. 19-31
Convergence of modified S-iteration process for two generalized asymptotically quasi-nonexpansive mappings in CAT(0) spaces
(naslov ne postoji na srpskom)
Department of Mathematics, Govt. Nagarjuna P.G. College of Science, Raipur, India

e-adresasaluja1963@gmail.com
Ključne reči: generalized asymptotically quasi-nonexpansive mapping; strong convergence; modified S-iteration process; common fixed point; CAT(0) space
Sažetak
(ne postoji na srpskom)
In this paper, we give the sufficient condition of newly defined modified S-iteration process to converge to common fixed point for two generalized asymptotically quasi-nonexpansive mappings in the framework of CAT(0) spaces. Also we establish some strong convergence theorems of the said iteration process and mappings under suitable conditions. Our results extend and improve many known results from the existing literature.
Reference
Agarwal, R.P., o'Regan D., Sahu, D.R. (2007) Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal., 8, 61-79
Bridson, M.R., Haefliger, A. (1999) Metric spaces of non-positive curvature. u: Grundlehren der Mathematischen Wissenschaften, Berlin, Germany: Springer, Vol. 319
Brown, K.S. (1989) Buildings. New York, NY, USA: Springer
Bruck, R., Kuczumow, T., Reich, S. (1993) Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. Colloquium Mathematicum, 65(2): 169-179
Bruhat, F., Tits, J. (1972) Groupes Réductifs Sur Un Corps Local. Publications mathématiques de l'IHÉS, 41(1): 5-251
Dhompongsa, S., Panyanak, B. (2008) On 4-convergence theorem in CAT(0) spaces. Comput. Math. Appl., 56(10); 2572-2579
Diaz, J.B., Metcalf, F.T. (1967) On the structure of the set of subsequential limit points of successive approximations. Bulletin of the American Mathematical Society, 73(4): 516-520
Fukhar-ud-din, H., Khan, S.H. (2007) Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications. Journal of Mathematical Analysis and Applications, 328(2): 821-829
Goebel, K., Kirk, W.A. (1972) A fixed point theorem for asymptotically nonexpansive mappings. Proceedings of the American Mathematical Society, 35(1): 171-171
Goebel, K., Reich, S. (1984) Uniform convexity, hyperbolic geometry, and nonexpansive mappings. u: Monographs and Textbooks in Pure and Applied Mathematics, New York, NY: Marcel Dekker Inc. USA, Vol. 83
Imnang, S., Suantai, S. (2009) Common Fixed Points of Multistep Noor Iterations with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings. Abstract and Applied Analysis, 2009: 1-14
Khamsi, M.A., Kirk, W.A. (2001) An introduction to metric spaces and fixed point theory. John Wiley & Sons
Khan, A.R., Khamsi, M.A., Fukhar-ud-din, H. (2011) Strong convergence of a general iteration scheme in spaces. Nonlinear Analysis: Theory, Methods & Applications, 74(3): 783-791
Khan, S.H., Abbas, M. (2011) Strong and 4-convergence of some iterative schemes in CAT(0) spaces. Comput. Math. Appl, Vol. 61(1), 109-116
Kirk, W.A. (2003) Geodesic geometry and fixed point theory. u: Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), University of Seville Secretary of Publications, Seville, Spain, Vol. 64 of Coleccion Abierta, 195-225
Kirk, W. (2004) Fixed point theorems in spaces and -trees. Fixed Point Theory and Applications, 2004(4): 738084
Niwongsa, Y., Panyanak, B. (2010) Noor iterations for asymptotically nonexpansive mappings in CAT(0) spaces. Int. J. Math. Anal, Vol. 4(13), 645-656
Qihou, L. (2001) Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings. Journal of Mathematical Analysis and Applications, 259(1): 1-7
Qihou, L. (2001) Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings with Error Member. Journal of Mathematical Analysis and Applications, 259(1): 18-24
Şahin, A., Başarır, M. (2013) 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, 2013(1): 12
Sahu, D.R., Jung, J.S. (2003) Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type. International Journal of Mathematics and Mathematical Sciences, 2003(33): 2075-2081
Saluja, G.S. (2007) Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space. Tamkang J. Math, 38(1), 85-92
Schu, J. (1991) Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 43(01): 153
Senter, H.F., Dotson, W.G. (1974) Approximating fixed points of nonexpansive mappings. Proceedings of the American Mathematical Society, 44(2): 375-375
Shahzad, N., Udomene, A. (2006) Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces. Fixed Point Theory and Applications, 2006: 1-10
Tan, K.K., Xu, H.K. (1993) Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications, 178(2): 301-308
Tan, K., Xu, H.K. (1994) Fixed point iteration processes for asymptotically nonexpansive mappings. Proceedings of the American Mathematical Society, 122(3): 733-733