Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces

Dhage, Bapurao C.

Research Article

Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces

Bapurao C. Dhage¹

kasubai, Gurukul Colony, Ahmedpur-413 515, Dist. Latur, Maharashtra, India

Abstract

In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968) and Bose and Mukherjee (1981) as the special cases with a different and constructive method.

How to Cite

B. C. Dhage, Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces, Int. J. Anal. Appl. 6 (2014), 144–153.

BibTeX

@article{Dhage2014,
  author  = {Dhage, Bapurao C.},
  title   = {Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {6},
  year    = {2014},
  pages   = {144--153},
  doi     = {}
}

References

[1] J. Bogin, A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad Math. Bull. 19 (1976),7-12.
[2] R. K. Bose, R. N. Mukherjee, Approximating fixed points if some mappings, Proc. Amer. Math. Soc. 82 (1981), 603-606.
[3] Lj. B. Ciric, On some nonexpansive type mapppings and fixed points, Indian J. Pure Appl. Math., 24 (1993), 145-149.
[4] B. C. Dhage, Generalized nonexpansive mappings and fixed points in metric spaces, (Submitted)
[5] W. C. Dotson Jr., Fixed points of quasi-nonexpansive mappings, J. Austral. Math. Soc. 13 (1972), 167-170.
[6] K. Goebel, W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press 1990.
[7] R. Kannan, Some reswults on fixed points, Bull. Cal. Math. Soc. 60 (1968), 71-76.
[8] W. R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc. 4 (1953), 506-510.
[9] H. F. Senter, W. G. Dotson, Approximating fixed points if nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-379.