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

Author

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  • 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
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    References listed on IDEAS

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    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.
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