On existence results in fixed set theory and applications to self-similarity



	On existence results in fixed set theory and applications to self-similarity


	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 $\displaystyle\sum_{i=1}^{p}A\cdot B_i$ , 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 $\left(\frac{I}{A}\right)$ , we obtain new fixed-set theorems for the operators of the form $\left(\frac{I}{A}\right)^{-1}\displaystyle\sum_{i=1}^{p}B_i$ under some suitable conditions on the operators A, B₁,..., B_p. 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. Abstract pdf Fulltext pdf Back to volume's table of contents