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A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b -Metric Spaces

Author

Listed:
  • Nayab Alamgir

    (School of Natural Sciences, National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan)

  • Quanita Kiran

    (School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan)

  • Hassen Aydi

    (Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
    China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Aiman Mukheimer

    (Department of Mathematics and General Sciences, Prince Sultan University Riyadh, Riyadh 11586, Saudi Arabia)

Abstract

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b -metric space U into the non empty closed and bounded subsets of U , which generalizes Nadler’s fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi–Takahashi’s type fixed point theorem for a multi-valued mapping from a complete extended b -metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature.

Suggested Citation

  • Nayab Alamgir & Quanita Kiran & Hassen Aydi & Aiman Mukheimer, 2019. "A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b -Metric Spaces," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:478-:d:234448
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    References listed on IDEAS

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    1. Nabil Mlaiki & Hassen Aydi & Nizar Souayah & Thabet Abdeljawad, 2018. "Controlled Metric Type Spaces and the Related Contraction Principle," Mathematics, MDPI, vol. 6(10), pages 1-7, October.
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    Cited by:

    1. N. Seshagiri Rao & Zoran D. Mitrović & Dania Santina & Nabil Mlaiki, 2023. "Fixed Point Theorems of Almost Generalized Contractive Mappings in b -Metric Spaces and an Application to Integral Equation," Mathematics, MDPI, vol. 11(11), pages 1-19, June.
    2. Md Hasanuzzaman & Salvatore Sessa & Mohammad Imdad & Waleed M. Alfaqih, 2020. "Fixed Point Results for a Selected Class of Multi-Valued Mappings under ( θ , ℛ )-Contractions with an Application," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    3. Vahid Parvaneh & Babak Mohammadi & Hassen Aydi & Aiman Mukheimer, 2019. "Generalized ( σ , ξ )-Contractions and Related Fixed Point Results in a P.M.S," Mathematics, MDPI, vol. 7(5), pages 1-14, May.

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