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Fixed Point Results for a Selected Class of Multi-Valued Mappings under ( θ , ℛ )-Contractions with an Application

Author

Listed:
  • Md Hasanuzzaman

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    These authors contributed equally to this work.)

  • Salvatore Sessa

    (Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
    These authors contributed equally to this work.)

  • Mohammad Imdad

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    These authors contributed equally to this work.)

  • Waleed M. Alfaqih

    (Department of Mathematics, Hajjah University, Hajjah 1729, Yemen
    These authors contributed equally to this work.)

Abstract

In this article, we introduce a relatively new concept of multi-valued ( θ , R ) -contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:695-:d:353203
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    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

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