Opuscula Math. 30, no. 3 (2010), 331-340
http://dx.doi.org/10.7494/OpMath.2010.30.3.331

 
Opuscula Mathematica

Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Gurucharan Singh Saluja
Hemant Kumar Nashine

Abstract. In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.

Keywords: implicit iteration process, finite family of asymptotically quasi-nonexpansive mappings, common fixed point, convex metric space.

Mathematics Subject Classification: 47H05, 47H09, 47H10.

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  • Gurucharan Singh Saluja
  • Govt. Nagarjun P.G. College of Science, Department of Mathematics & Information Technology, Raipur (Chhattisgarh), India
  • Hemant Kumar Nashine
  • Disha Institute of Management and Technology, Department of Mathematics Satya Vihar, Vidhansabha - Chandrakhuri Marg (Baloda Bazar Road), Mandir Hasaud, Raipur - 492101(Chhattisgarh), India
  • Received: 2010-01-04.
  • Accepted: 2010-02-21.
Opuscula Mathematica - cover

Cite this article as:
Gurucharan Singh Saluja, Hemant Kumar Nashine, Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces, Opuscula Math. 30, no. 3 (2010), 331-340, http://dx.doi.org/10.7494/OpMath.2010.30.3.331

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