A Study on p-Cyclic Orbital Geraghty type Contractions

Authors

  • M. L.Suresh
  • T. Gunasekar
  • S. Karpagam
  • B. Zlatanov
  • . .

DOI:

https://doi.org/10.14419/ijet.v7i4.10.26780

Published:

2018-10-02

Keywords:

p-cyclic maps, Orbital contraction, Geraghty type contraction.

Abstract

Consider a metric space  and the non empty sub sets, of X. A map called p-cyclic orbital Geraghty type of contraction is introduced.  Convergence of a unique fixed point and a best proximity point for this map is obtained in a uniformly convex Banach space setting.  Also, this best proximity point is the unique periodic point of such a map.

 

 

References

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[3] A.Eldred, Existence and Convergence of Best proximity points, Ph.D Thesis, 2006, Indian Institute of Technology Madras, Chennai, India.

[4] S. Karpagam, On fixed point theorems and best proximity point theorems, Ph.D Thesis 2009, The Ramanujan Institute for Advanced study in Mathematics, University of Madras, Chennai , Indai.

[5] S. Karpagam and S. Agrawal, Best proximity point theorems for cyclic orbital Meir- Keeler contraction maps, Nonlinear Anal. 74 (2011) 1040-1046.

[6] S. Karpagam and S. Agrawal, Best Proximity point for p-cyclic Meir- Keeler contractions, Fixed Point Theory Appl., Volume 29, Article ID 197308, 9 pages.

[7] S. Karpgam and S. Agrawal, Existence of best proximity points for p- cyclic contractions, Fixed point Theory, 13 :99 - 105, 2012.

[8] M. Petric, BZlatanov, Best proximity points and Fixed points for p- summing maps, Fixed point theory appl., 2012:2012:86

[9] B. Zlatanov, Best Proximity points for p- Summing Cyclic Orbital Meir - Keeler Contractions, Nonlinear Anal. Model. Control 20 (4) 2015 528-544.

[10] S. Karpagam and B. Zlztanov, Best proximity points of p-cyclic orbital Meir - Keeler contraction maps, Nonlinear Anal. Model. Control, 21 (6) :790 -806,2016.

[11] S. Karpagam and B. Zlatanov, A note on p- summing orbital Meir - Keeler contraction maps, Int. J. Pure and Applied Math. Volume 107 no. 1, 2016, 225-243.

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How to Cite

L.Suresh, M., Gunasekar, T., Karpagam, S., Zlatanov, B., & ., . (2018). A Study on p-Cyclic Orbital Geraghty type Contractions. International Journal of Engineering & Technology, 7(4.10), 883–887. https://doi.org/10.14419/ijet.v7i4.10.26780

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Received 2019-01-30
Accepted 2019-01-30
Published 2018-10-02