Volume-10 , Issue-3 , Jun 2023, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Some Fixed-Point Theorems For Contractive Type Mappings In Metric Spaces

  Barnita Bharati, Kalishankar Tiwary

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.3 , pp.68-73, Jun-2023

  Abstract

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  Abstract
  There are two sections in the present paper. In first section some theorems have been proved in metric spaces which generalize the results proved in [5], [10], [12], [15], [16] and in the second section theorems relating to fixed points for densifying mappings which will be explained in the section 2.

  Key-Words / Index Term
  Contractive type mapping, Densifying mapping, well locally contractiveness, Fixed point, Metric space.

  References
  [1] Ciric, Ljubomir, On locally contractive fixed point mapping, Fundamenta, 120, No. 3, 223-228, 1984.
  [2] Darbo, G., Punti Uniti in transformations a condionio non-compactie, Rend. Sem. Mat. Univ. Padova, 24, 84-92, 1955.
  [3] Edelstein, M., On fixed and periodic points under contractive mappings, J. London Math. Soc., 37, 74-79, 1962.
  [4] Furi, M and Vignoli, A., A fixed point theorem in a complete metric space, Boll U. M. I., 4, 505-509, 1969.
  [5] Iseki, K., Fixed point theorem for densifying mapping, Math. Sem. Notes, Kobe University, 2, 70-74, 1974.
  [6] Kalishankar Tiwary, Biplab Kumar Bag, Chandan Kamelia, "Common Fixed-Point Theorems in Complete Hausdörff Uniform Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.84-88, 2019
  [7] Kalishankar Tiwary, Chandan Kamelia, Biplab Kumar Bag, "On Common Fixed Points of Mappings in Hilbert Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.100-103, 2019
  [8] Krishnadhan Sarkar, Dinanath Barman, Mithun Paul, Kalishankar Tiwary, "Probabilistic Metric Space, Menger Space and Some Common Fixed Point Theorem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.5, pp.86-90, 2019
  [9] Kuratowski, C., Surles espaces complete, Fund. Math., 15, 301-309, 1930.
  [10] Mainak Mitra, Jigmi Dorjee Bhutia, Kalishankar Tiwary, "On the Existence of Common Fixed Point in a Complete Metric Space Using Integral Type Contraction Conditions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.25-35, 2022
  [11] Nusabaum, R. D., The fixed point index for local condensing map, Aun. Mat.Pune Applied, 89, 217-258, 1971.
  [12] Singh, G.N. and Tiwary, Kalishankar: A fixed point theorem, The Mathematics Education, 28, 94-102, 1994.
  [13] Tarun Gain, Kalishankar Tiwary, "Some Common Fixed Point Theorems in 2-Metric Spaces for Contractive Type Conditions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.58-61, 2019
  [14] Tiwary, Kalishankar and Debnath, S.C., A fixed point theorem for densifying mapping in a complete metric space, J. Ind., Acad. Math., 17, 2, 146-149, 1995.
  [15] Tiwary, Kalishankar and Kundu, Anjana, Some fixed point theorems for contractive type mappings, Acta Ciencia Indica, Vol. XXX M, No. 4, 849, 2004.
  [16] Tiwary, Kalishankar and Lahiri, B.K., Fixed point theorem for generalised well locally contractive mappings, Ranchi University, Maths., 19, 77-86, 1988.
  [17] Wong, C.S., Generalised contraction and fixed-point theorems, Proc. Amer. Math. Soc., 42, 409-417, 1974.

  Citation
  Barnita Bharati, Kalishankar Tiwary, "Some Fixed-Point Theorems For Contractive Type Mappings In Metric Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.3, pp.68-73, 2023