caa a22 4500 605508909 CHVBK 20210128100638.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00010-014-0309-z doi (NATIONALLICENCE)springer-10.1007/s00010-014-0309-z On two functional equations with involution on groups related to sine and cosine functions [Elektronische Daten] [Allison Perkins, Prasanna Sahoo] Let G be a group, $${\mathbb{C}}$$ C be the field of complex numbers, z 0 be any fixed, nonzero element in the center Z(G) of the group G, and $${\sigma : G \to G}$$ σ : G → G be an involution. The main goals of this paper are to study the functional equations $${f(x{\sigma}yz_{0}) - f(xyz_{0}) = 2f(x)f(y)}$$ f ( x σ y z 0 ) - f ( x y z 0 ) = 2 f ( x ) f ( y ) and $${f(x{\sigma}yz_{0}) + f(xyz_{0}) = 2f(x)f(y)}$$ f ( x σ y z 0 ) + f ( x y z 0 ) = 2 f ( x ) f ( y ) for all $${x, y \in G}$$ x , y ∈ G and some fixed element z 0 in the center Z(G) of the group G. Springer Basel, 2014 Abelian function nationallicence involution nationallicence Kannappan's functional equation nationallicence Van Vleck's functional equation nationallicence group character nationallicence Perkins Allison Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA aut Sahoo Prasanna Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA aut Aequationes mathematicae Springer Basel 89/5(2015-10-01), 1251-1263 0001-9054 89:5<1251 2015 89 10 https://doi.org/10.1007/s00010-014-0309-z 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/s00010-014-0309-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Perkins Allison Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA aut NATIONALLICENCE 700 1- Sahoo Prasanna Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/5(2015-10-01), 1251-1263 0001-9054 89:5<1251 2015 89 10