On a generalization of the Popoviciu equation on groups

Małgorzata Chudziak

Abstract


We determine a general solution of the Popoviciu type functional equation on groups.

Keywords


Popoviciu equation; quadratic equation; additive function

Mathematics Subject Classification


39B22

References


Brzdęk, J. "A note on stability of the Popoviciu functional equation on restricted domain." Demonstratio Math. 43.3 (2010): 635-641.

Kannappan, P. "Quadratic functional equation and inner product spaces." Results Math. 27 (1995): 368-372.

Lee, Y.W. "On the stability on a quadratic Jensen type functional equation." J. Math. Anal. Appl. 270 (2002): 590-601.

---. "Stability of a generalized quadratic functional equation with Jensen type." Bull. Korean Math. Soc. 42 (2005): 57-73.

Popoviciu, T. "Sur certaines inégalités qui caractérisentes fonctions convexes." An. Sti. Univ. "Al. I. Cuza" Iasi Sect. I a Mat. (N.S.) 11 (1965): 155-164.

Smajdor, W. "Note on a Jensen type functional equation." Publ. Math. Debrecen 63 (2003): 703-714.

Trif, T. "Hyers-Ulam-Rassias stability of a Jensen type functional equation." J. Math. Anal. Appl. 250 (2000): 579-588.

---. "On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions." J. Math. Anal. Appl. 272 (2002): 604-616.


Full Text: PDF

Download statistics: 2707



e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej