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Set valued Reich type G-contractions in a complete metric space with graph

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Abstract

In this paper, set valued Reich type G-contractions are introduced in the framework of a complete metric space equipped with graph. Existence and uniqueness of fixed points for these contractions are established. We provide the graph version of Reich’s theorems for set valued mappings. Further, Kannan’s theorem in this context has been stated as a consequence. Examples have been constructed to signify the validity of our results.

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Acknowledgements

The authors are immensely thankful the reviewers and the Editor for their remarkable suggestions towards improvement of the manuscript.

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Authors and Affiliations

  1. Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam, 788011, India

    Pradip Debnath

  2. Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh, 791109, India

    Murchana Neog

  3. Department of Mathematics, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia

    Stojan Radenović

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  1. Pradip Debnath
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  2. Murchana Neog
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  3. Stojan Radenović
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Pradip Debnath.

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Debnath, P., Neog, M. & Radenović, S. Set valued Reich type G-contractions in a complete metric space with graph. Rend. Circ. Mat. Palermo, II. Ser 69, 917–924 (2020). https://doi.org/10.1007/s12215-019-00446-9

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