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Fixed point sets of multivalued rational contractions with stability analysis

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Abstract

The present paper is on fixed point theory in set valued analysis. Here putting several concepts together, we define a set valued contraction and establish that such contractions have fixed points in a complete metric space. We have two main theorems in one of which we use \(\alpha \)-regularity condition of the space as a substitute of the continuity requirement on the multivalued contraction. There are some illustrative examples and corollaries. We also perform stability analysis of fixed point sets. We establish that the fixed point sets associated with the mappings we consider in our theorems are stable. In the last section we discuss some consequences of the main results of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, 711103, India

    Binayak S. Choudhury

  2. Department of Mathematics, Sovarani Memorial College, Jagatballavpur, Howrah, West Bengal, 711408, India

    Nikhilesh Metiya

  3. Department of Mathematics, Government General Degree College, Salboni Paschim Medinipur, West Bengal, 721516, India

    Sunirmal Kundu

Authors
  1. Binayak S. Choudhury
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  2. Nikhilesh Metiya
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  3. Sunirmal Kundu
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Correspondence to Nikhilesh Metiya.

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Choudhury, B.S., Metiya, N. & Kundu, S. Fixed point sets of multivalued rational contractions with stability analysis. Afr. Mat. 34, 87 (2023). https://doi.org/10.1007/s13370-023-01109-w

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