On orthogonally additive functions with orthogonally additive second iterate

• Autorzy: Baron K.

Identyfikatory

DOI

10.14708/cm.v53i2.799

• Języki publikacji: EN

Abstrakty

EN

Let E be a real inner product space of dimension at least 2. If f maps E onto E and both f and f∘f are orthogonally additive, then f is additive.

Słowa kluczowe

EN

orthogonally additive and additive function; inner product space; iterate

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 301--304
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Baron K.

• Instytut Matematyki Uniwersytetu Śląskiego, Bankowa 14, 40–007 Katowice, Poland

Bibliografia

• [1] K. Baron, On some orthogonally additive functions on inner product spaces, Ann. Univ. Budapest. Sect. Comput. 40 (2013), 123-127.
• [2] K. Baron and A. Kucia, On regularity of functions connected with orthogonal additivity, Func. Approx. Comment. Math. 26 (1998), 19-24.
• [3] K. Baron and J. Rätz, On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187-189.
• [4] M. Kuczma, An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality, second edition (edited by A. Gilányi), Birkhäuser Verlag, Basel, 2009.
• [5] J. Rätz, On orthogonally additive mappings, Aequationes Math. 28 (1985), 35-49.