IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i8p754-d258649.html
   My bibliography  Save this article

Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph

Author

Listed:
  • Reny George

    (Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarh 490006, India)

  • Hossam A. Nabwey

    (Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Basic Engineering Sciences, Faculty of Engineering, Menofia University, Shebin El-Kom, Menofia 32511, Egypt)

  • Rajagopalan Ramaswamy

    (Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

  • Stojan Radenović

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
    Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia)

Abstract

We have introduced the new notions of R -weakly graph preserving and R -weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S , α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b -metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R -weakly α -admissible pair of multivalued mappings in a b -metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.

Suggested Citation

  • Reny George & Hossam A. Nabwey & Rajagopalan Ramaswamy & Stojan Radenović, 2019. "Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph," Mathematics, MDPI, vol. 7(8), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:754-:d:258649
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/8/754/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/8/754/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Haitham Qawaqneh & Mohd Salmi Md Noorani & Wasfi Shatanawi & Hassen Aydi & Habes Alsamir, 2019. "Fixed Point Results for Multi-Valued Contractions in b −Metric Spaces and an Application," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:754-:d:258649. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.