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Fixed Points, Fixed Sets and Iterated Multifunction Systems for Nonself Multivalued Operators

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Abstract

In this paper, we will present some fixed set and fixed point theorems for nonself multivalued generalized contractions. We will discuss the cases of multivalued contractions, multivalued φ-contractions and multivalued Kannan contractions. Our results propose some existence, uniqueness and related properties of the multivalued fractal generated by iterative multifunction systems. The approach is based on some new properties proved for the multi-fractal operator induced by a nonself multivalued generalized contraction. Some open problems are also formulated.

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Authors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University of Cluj-Napoca, Kogălniceanu Street, No.1, 400084, Cluj-Napoca, Romania

    Adrian Petruşel, Ioan A. Rus & Marcel-Adrian Şerban

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  1. Adrian Petruşel
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  2. Ioan A. Rus
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  3. Marcel-Adrian Şerban
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Correspondence to Adrian Petruşel.

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Petruşel, A., Rus, I.A. & Şerban, MA. Fixed Points, Fixed Sets and Iterated Multifunction Systems for Nonself Multivalued Operators. Set-Valued Var. Anal 23, 223–237 (2015). https://doi.org/10.1007/s11228-014-0291-6

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