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Existence, data-dependence and stability of coupled fixed point sets of some multivalued operators

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  • Choudhury, Binayak S.
  • Metiya, Nikhilesh
  • Kundu, Sunirmal

Abstract

In this work we consider a fixed point problem related to a multivalued coupled mapping which we define here. The function is also assumed to satisfy α- dominating condition which is a conceptual extension of admissibility condition. We show that the fixed point problem is solvable for the case of the mapping we consider here. Further we examine the data-dependence and stability of fixed point sets associated with the coupled multivalued mapping. The main result is deduced in metric spaces. Its consequences are discussed in partially ordered metric spaces as well as in metric spaces with a graph. There are some illustrative examples. The work is in the domain of setvalued analysis.

Suggested Citation

  • Choudhury, Binayak S. & Metiya, Nikhilesh & Kundu, Sunirmal, 2020. "Existence, data-dependence and stability of coupled fixed point sets of some multivalued operators," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300801
    DOI: 10.1016/j.chaos.2020.109678
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    References listed on IDEAS

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    1. Erdal Karapınar & Bessem Samet, 2012. "Generalized 𠜶 - ð Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, September.
    2. Binayak S. Choudhury & Nikhilesh Metiya & Pradip Debnath, 2016. "End Point Results in Metric Spaces Endowed with a Graph," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, October.
    3. Pushpendra Semwal & Ramesh Chandra Dimri, 2014. "A Suzuki Type Coupled Fixed Point Theorem for Generalized Multivalued Mapping," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
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    Cited by:

    1. Choudhury, Binayak S. & Chakraborty, Priyam, 2022. "Strong fixed points of Φ-couplings and generation of fractals," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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