Convergence theorems for generalized asymptotically quasi-nonexpansive mappings in cone metric spaces

• G. S Saluja ^[1]
  1. [1] Govt. Nagarjuna P.G. College of Science Department of Mathematics and Information Technology
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 15, Nº. 3, 2013, págs. 71-88
• Idioma: inglés
• DOI: 10.4067/S0719-06462013000300008
• Enlaces
  • Texto completo
• Resumen
  • español

    El propósito de este artículo es estudiar el proceso de iteración del tipo Ishikawa con errores para aproximar el puto fijo común de dos aplicaciones cuasi-expansivas asintéticamente generalizadas en el marco de espacios métricos cónicos. Nuestro resultado extiende y generaliza muchos resultados de la literatura existente.

  • English

    The purpose of this paper is to study an Ishikawa type iteration process with errors to approximate the common fixed point of two generalized asymptotically quasinonexpansive mappings in the framework of cone metric spaces. Our results extend and generalize many known results from the existing literature.

• Referencias bibliográficas
  • Abbas, M,Rhoades, B.E. (2009). Fixed and periodic point results in cone metric spaces. Appl. Math. Lett. 22. 511-515
  • Agarwal, R.P,O'Regan, D,Precup, R. (2007). Domain invariance theorems for contractive type maps. Dynam. Syst. Appl. 16. 579-586
  • Asadi, M,Soleimani, H,Vaezpour, S.M. (2009). An order on subsets of cone metric spaces and fixed points of set valued contractions. Fixed...
  • Bose, S.C. (1978). Common fixed points of mappings in a uniformly convex Banach space. J. London Math. Soc. 18. 151-156
  • Chang, S.S,Kim, J.K,Jin, D.S. (2004). Iterative sequences with errors for asymptotically quasi-nonexpansive type mappings in convex metric...
  • Ciri, L.B. (1971). Generalized contractions and fixed point theorems. Publicationsde l'Institut Mathematique, Nouvelle Serie. 12. 19-26
  • Deimling, K. (1985). Nonlinear Functional Analysis. Springer. Berlin.
  • Duki, D,Paunovic, L,Radenovic, S. (2011). Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces....
  • Fukhar-ud-din, H,Khan, S.H. (2007). Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications. J....
  • Huang, L.-G,Zhang, X. (2007). Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332. 1468-1476
  • Ilic, D,Rakocevic, V. (2009). Quasi-contraction on a cone metric space. Appl. Math. Lett. 22. 728-731
  • Imnang, S,Suantai, S. (2009). Common fixed points of multi-step Noor iterations with errors for a finite family of generalized asymptotically...
  • Jankovic, S,Kadelburg, Z,Radenovic, S,Rhoades, B.E. Assad-Fixed-Type point theorems for a pair of nonself mappings on cone metric spaces....
  • Jeong, J.U,Kim, S.H. (2006). Weak and strong onvergence of the Ishikawa iteration process with errors for two asymptotically nonexpansive...
  • Kim, J.K,Kim, K.H,Kim, K.S. (2004). Convergence theorems of modified three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive...
  • Kim, J.K,Kim, K.H,Kim, K.S. (2004). Three-step iterative sequences with errors for asymptotically quasi-nonexpansive mappings in convex metric...
  • Lin, S.D. (1987). A common fixed point theorem in abstract spaces. Indian J. Pure Appl. Math. 18. 685-690
  • Liu, Q.H. (2001). Iterative sequences for asymptotically quasi-nonexpansive mappings. J. Math. Anal. Appl. 259. 1-7
  • Liu, Q.H. (2001). Iterative sequences for asymptotically quasi-nonexpansive mappings with error member. J. Math. Anal. Appl. 259. 18-24
  • Petrusel, G,Petrusel, A. (2008). Multivalued contractions of Feng-Liu type in complete gauge spaces. Carpth. J. Math. Anal. Appl. 24. 392-396
  • Petrusel, A. (2001). Generalized multivalued contractions. Nonlinear Anal. (TMA). 47. 649-659
  • Radenovi, S,Rhoades, B.E. (2009). Fixed point theorem for two non-self mappings in cone metric spaces. Comput. Math. Appl. 57. 1701-1707
  • Rzepecki, B. (1980). On fixed point theorems of Maia type. Publicationsde l'Institut Mathematique, Nouvelle Serie. 28. 179-186
  • Rezapour, Sh. A review on topological properties of cone metric spaces. Proceedings of the International Conference on Analysis, Topology...
  • Rezapour, Sh,Hamlbarani, R. (2008). Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings. J. Math....
  • Takahashi, W. (1970). A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22. 142-149
  • Tian, Y.-X. (2005). convergence of an Ishikawa type iterative scheme for asymptotically nonexpansive mappings. Comput. Math. Appl. 49. 1905-1912
  • Vandergraft, J. (1967). Newton method for convex operators in partially ordered spaces. SIAM J. Numer. Anal. 4. 406-432
  • Wang, C,Liu, L. (2009). Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces. Nonlinear...
  • Wang, C,Zhu, J,Damjanovic, B,Hu, L. (2009). Approximating fixed points of a pair of contractive type mappings in generalized cone metric spaces....
  • Wang, C,Li, J,Zhu, D. Convergence theorems for the unique common fixed point of a pair of asymptotically nonexpansive mappings in generalized...
  • Wardowski, D. (2009). Endpoints and fixed points of set-valued contractions in cone metric spaces. Nonlinear Anal. (TMA). 71. 512-516
  • Zabrejko, P.P. (1997). K-metric and K-normed linear spaces: survey. Collectanea Mathematica. 48. 825-859