Selections of generalized convex set-valued functions with bounded diameter


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	Selections of generalized convex set-valued functions with bounded diameter


	Fixed Point Theory, Volume 18, No. 1, 2017, 375-384, March 1st, 2017 DOI: 10.24193/fpt-ro.2017.1.29 Authors: Andrzej Smajdor and Joanna Szczawińska Abstract: Applying the classical Banach fixed point theorem we prove that a set-valued function with bounded diameter satisfying a linear functional inclusion admits a unique selection fulfilling the corresponding functional equation. We also adopt the method of the proof for investigating the Hyers-Ulam stability of some functional equations. Key Words and Phrases: Subadditive set-valued function, stability, fixed point. 2010 Mathematics Subject Classification: 54C65, 28B20, 47H10, 39B82. Published on-line: March 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents