On Hyers-Ulam stability of Wilson's functional equation on $P_3$-groups
DOI:
https://doi.org/10.5644/SJM.03.2.07Keywords:
Hyers-Ulam stability, Wilson’s equation, $P_3$-groupAbstract
The purposes of paper is to obtain the Hyers-Ulam stability of Wilson’s equation...
2000 Mathematics Subject Classification. Primary 39B52; Secondary 20B99
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References
J. Acz´el and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.
J. Acz´el, J. K. Chung and C. T. Ng, Symmetric second differences in product form on groups, in: Th. M. Rassias (Ed.), Topics in mathematical analysis, 1–22, Ser. Pure Math. 11, World Scientifc, Singapore-Teaneck, N. Y., 1989.
R. Badora, On a joint generalization of Cauchy’s and d’Alembert’s functional equations, Aequationes Math., 43 (1992), 72–89.
R. Badora, On Hyers-Ulam stability of Wilson’s functional equation, Aequationes Math., 60 (2000) 211–218.
J. A. Baker, The stability of the cosine functional equation, Proc. Amer. Math. Soc., 80 (1980), 411–416.
W. Chojnacki, On some functional equation generalizing Cauchy’s and d’Alembert’s functional equation, Colloq. Math., 55 (1988), 169–178.
J. K. Chung, Pl. Kannappan and C. T. Ng, A generalization of the cosine-sine functional equation on groups, Linear Algebra and its Application, 66 (1985), 259–277.
I. Corovei, The functional equation f(xy) + f(yx) + f(xy−1) + f(y−1x) = 4f(x)f(y) for nilpotent groups, Bul. St¸iint¸. Inst. Politechn. Cluj-Napoca Ser. Mat. Apl. Mec., 20 (1977), 25–28.
I. Corovei, The functional equation f(xy)+f(xy−1) = 2f(x)f(y) for nilpotent groups, Mathematica (Cluj), 22 (45) (1980), 33–41.
I. Corovei, The d’Alembert functional equation on metabelian groups, Aequationes Math., 57 (1999), 201–205.
I. Corovei, Wilson’s functional equation on P3-groups, Aequationes Math., 61 (2001) 212–220.
W. F¨org-Rob and J. Schwaiger, The stability of some functional equations for generalized hyperbolic functions and for the generalized cosine equation, Results in Math., 26 (1994), 274–280.
D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, Basel, Berlin, 1998.
S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Inc., Palm Harbor, Florida, 2001.
R. C. Penney and A. L. Rukhin, D’Alembert’s functional equation on groups, Proc. Amer. Math. Soc., 77 (1979), 73–80.
P. Sinopoulos, Wilson’s functional equation for vector and matrix functions, Proc. Amer. Math. Soc., 127 (1997), 1089–1094.
H. Stetkaer, D’Alembert’s equation and spherical functions, Aequationes Math., 48 (1994), 220–227.
H. Stetkaer, Wilson’s functional equations on groups, Aequationes Math., 49 (1995), 252–275.
