Chitkara University Publications

Unique Fixed Point Theorem for Weakly Inward Contractions and Fixed Point Curve in 2-Banach Space

Abstract:

In this paper, we prove unique fixed point theorem for weakly inward contractions on 2-Banach space and introduce the concept of fixed point curve in 2-Banach space.
2010 AMS Classification: 41A65, 46B20,47H10, 54H25.

Author(s):

  • P Riyas, Department of Mathematics, K M M Govt. Women’s College, Kannur, India-670004
  • KT Ravindran, P G Department of Mathematics, Payyannur College, Kannur, India

DOI: 

Keywords: 

2-normed space, 2-Banach Space, fixed point, weakly inward contraction, fixed point curve.

References:

F Raymond and Y J Cho, Geometry of Linear 2-Normed Space, Nova Science Publishers, Inc. Hauppauge, Ny(2001).

K Iseki, Fixed point theorems in 2-Banach Spaces, Math Seminar Notes, Kobe Univ, 2(1976),11-13.

Mehmet Kir and Hukmi Kiziltunc, Some New Fixed Point Theorems in 2-Normed Space, Int. Journal of Math. Analysis. Vol.7(2013).

P K Harikrishnan and K T Ravindran, Some Properties of Accretive operators in Linear 2-Normed Spaces, International Mathematical Forum, vol.6, (2011) no.59, 2941-2947.

P. Riyas and K. T. Ravindran, Fixed Point Curve for Weakly Inward Contractions and Approximate Fixed Point Property, Anal. Theory Appl., 29 (2013), pp. 342-347.

R P Agarwal, Donal O Regan, D R Sahu Fixed Point Theory for Lip- schitzian Type Mappings with Applications Springer Science, Business Media, LLC(2009).

S. Gähler, Lineare 2- normierte Rume, Math.Nachr.28(1964)1-43.

S. Gähler, Uber 2-Banach räume, Math. Nachr., 42(1969), 335-347. http://dx.doi.org/10.1002/mana.19690420402

Sam B Nadler, K Ushijima, Fixed Point Curves for Linear Interpolations of Contraction Maps, Applicable Analysis, Vol-29,1988.

Siddiqi, A.H., 2-normed spaces, Aligarh Bull. math., (1980), 53-70.

T. Vidali, Fixed Point Curve Generated by Nonexpansive Mappings, Fixed Point Theory, Volume 6, No 2.2205,333-339.

 

 

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