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On existence results in fixed set theory and applications to self-similarity | |
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Fixed Point Theory, Volume 23, No. 1, 2022, 85-104, February 1st, 2022 DOI: 10.24193/fpt-ro.2022.1.06 Authors: Khaled Ben Amara, Aref Jeribi and Najib Kaddachi Abstract: In this manuscript, by removing the domain convexity hypothesis, the existence of fixed set results for the sum and the product of (p+1)-multi-valued operators , acting on Banach algebras satisfying a sequential condition 𝓟 under weak topology is proved. In addition, by using a new definition of the multi-valued operator , we obtain new fixed-set theorems for the operators of the form under some suitable conditions on the operators A, B1,..., Bp. Applications to self-similarity theory are also given. Key Words and Phrases: Banach algebra, weakly sequentially continuous, measure of weak non-compactness, fixed-set theory. 2010 Mathematics Subject Classification: 47H10, 45G15. Published on-line: February 1st, 2022.
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