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On p -Cyclic Orbital M-K Contractions in a Partial Metric Space

Author

Listed:
  • Tharmalingam Gunasekar

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600 062, Tamil Nadu, India)

  • Saravanan Karpagam

    (Department of Science and Humanities, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602 105, India)

  • Boyan Zlatanov

    (Faculty of Mathematics and Informatics, University of Plovdiv, “Paisii Hilendarski”, 24 Tzar Assen str., Plovdiv 4000, Bulgaria)

Abstract

A cyclic map with a contractive type of condition called p -cyclic orbital M-Kcontraction is introduced in a partial metric space. Sufficient conditions for the existence and uniqueness of fixed points and the best proximity points for these maps in complete partial metric spaces are obtained. Furthermore, a necessary and sufficient condition for the completeness of partial metric spaces is given. The results are illustrated with an example.

Suggested Citation

  • Tharmalingam Gunasekar & Saravanan Karpagam & Boyan Zlatanov, 2018. "On p -Cyclic Orbital M-K Contractions in a Partial Metric Space," Mathematics, MDPI, vol. 6(7), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:7:p:116-:d:157004
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    References listed on IDEAS

    as
    1. Erdal Karapınar & I. Savas Yuce, 2012. "Fixed Point Theory for Cyclic Generalized Weak 𠜙 -Contraction on Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, July.
    2. Hassen Aydi & Erdal Karapinar, 2012. "A Fixed Point Result for Boyd-Wong Cyclic Contractions in Partial Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, July.
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    Cited by:

    1. Hind Alamri & Nawab Hussain & Ishak Altun, 2023. "Proximity Point Results for Generalized p -Cyclic Reich Contractions: An Application to Solving Integral Equations," Mathematics, MDPI, vol. 11(23), pages 1-25, November.
    2. Erdal Karapınar & Ravi P. Agarwal & Seher Sultan Yeşilkaya & Chao Wang, 2022. "Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey," Mathematics, MDPI, vol. 10(17), pages 1-76, August.

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