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Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey

Author

Listed:
  • Erdal Karapınar

    (Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot 75000, Vietnam
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics, Çankaya University, Etimesgut, Ankara 06790, Turkey)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA)

  • Seher Sultan Yeşilkaya

    (Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot 75000, Vietnam)

  • Chao Wang

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

Abstract

In this paper, we aim to review Meir–Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M -metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler’s contraction.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3109-:d:901277
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    References listed on IDEAS

    as
    1. Erdal Karapinar & Ravi Agarwal & Hassen Aydi, 2018. "Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces," Mathematics, MDPI, vol. 6(11), pages 1-7, November.
    2. Hassen Aydi & Erdal Karapınar & Shahram Rezapour, 2012. "A Generalized Meir-Keeler-Type Contraction on Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, April.
    3. Jelena Vujaković & Hassen Aydi & Stojan Radenović & Aiman Mukheimer, 2019. "Some Remarks and New Results in Ordered Partial b -Metric Spaces," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    4. Saleh A. Al-Mezel & Chi-Ming Chen & Erdal Karapınar & Vladimir Rakočević, 2014. "Fixed Point Results for Various -Admissible Contractive Mappings on Metric-Like Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, May.
    5. Badr Alqahtani & Andreea Fulga & Erdal Karapınar & Panda Sumati Kumari, 2019. "Sehgal Type Contractions on Dislocated Spaces," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    6. Nawab Hussain & Zoran Kadelburg & Stojan Radenović & Falleh Al-Solamy, 2012. "Comparison Functions and Fixed Point Results in Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, June.
    7. Erdal Karapınar & Chi-Ming Chen & Chih-Te Lee, 2019. "Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces," Mathematics, MDPI, vol. 7(4), pages 1-11, April.
    8. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    9. 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.
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