caa a22 4500 606200975 CHVBK 20210128100946.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00025-014-0416-0 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0416-0 Khodaei Hamid Department of Mathematics, Malayer University, P.O. Box 65719-95863, Malayer, Iran aut On the Stability of Additive, Quadratic, Cubic and Quartic Set-valued Functional Equations [Elektronische Daten] [Hamid Khodaei] For m=1, 2, 3, 4, we study the following set-valued functional equation $$\begin{array}{ll}f(ax + y) \oplus f(ax - y) = a^{m-2}[f(x + y) \oplus f(x - y)] \oplus 2(a^{2} - 1) [a^{m-2}f(x) \\ \quad \oplus \frac{(m - 2)(1 - (m - 2)^{2})}{6}f(y)]\end{array}$$ f ( a x + y ) ⊕ f ( a x - y ) = a m - 2 [ f ( x + y ) ⊕ f ( x - y ) ] ⊕ 2 ( a 2 - 1 ) [ a m - 2 f ( x ) ⊕ ( m - 2 ) ( 1 - ( m - 2 ) 2 ) 6 f ( y ) ] where a is a fixed positive integer with a>1. We also prove the stability of this set-valued functional equation by using the Banach fixed point theorem. Springer Basel, 2014 Set-valued map nationallicence contractively subhomogeneous map nationallicence expansively superhomogeneous map nationallicence stability nationallicence fixed point nationallicence Results in Mathematics Springer Basel 68/1-2(2015-09-01), 1-10 1422-6383 68:1-2<1 2015 68 25 https://doi.org/10.1007/s00025-014-0416-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0416-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Khodaei Hamid Department of Mathematics, Malayer University, P.O. Box 65719-95863, Malayer, Iran aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/1-2(2015-09-01), 1-10 1422-6383 68:1-2<1 2015 68 25