On a Sine Functional Equation

1963 ◽  
Vol 70 (3) ◽  
pp. 306 ◽  
Author(s):  
Sanford L. Segal
Keyword(s):  
Functional Equation ◽  
Sine Functional Equation

A sine functional equation

1970 ◽  
Vol 4 (1-2) ◽  
pp. 56-62 ◽  
Author(s):  
J. A. Baker
Keyword(s):  
Functional Equation ◽  
Sine Functional Equation

ON THE SUPERSTABILITY OF THE PEXIDER TYPE SINE FUNCTIONAL EQUATION

2012 ◽  
Vol 25 (1) ◽  
pp. 1-18
Author(s):  
Gwang Hui Kim
Keyword(s):  
Functional Equation ◽  
Sine Functional Equation

scholarly journals The Cosine-Sine Functional Equation on Semigroups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Bruce Ebanks
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Direct Solution ◽  
Continuous Solutions ◽  
Topological Semigroups ◽  
Primary Object ◽  
Object Of Study ◽  
Special Case ◽  
Sine Functional Equation

Abstract The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup. The name refers to the fact that it contains both the sine and cosine addition laws. This equation has been solved on groups and on semigroups generated by their squares. Here we find the solutions on a larger class of semigroups and discuss the obstacles to finding a general solution for all semigroups. Examples are given to illustrate both the results and the obstacles. We also discuss the special case f(xy) = f(x)g(y) + g(x)f(y) − g(x)g(y) separately, since it has an independent direct solution on a general semigroup. We give the continuous solutions on topological semigroups for both equations.

scholarly journals Stability of the Cosine–Sine Functional Equation on Amenable Groups

2020 ◽  
pp. 355-378
Author(s):  
Ajebbar Omar ◽  
Elqorachi Elhoucien
Keyword(s):  
Functional Equation ◽  
Amenable Groups ◽  
Sine Functional Equation

A functional inequality for entire functions generalizing the sine functional equation

1974 ◽  
Vol 10 (2-3) ◽  
pp. 318-318
Author(s):  
Lawrence Etigson
Keyword(s):  
Functional Equation ◽  
Entire Functions ◽  
Functional Inequality ◽  
Sine Functional Equation

scholarly journals A generalization of the cosine-sine functional equation on groups

1985 ◽  
Vol 66 ◽  
pp. 259-277 ◽  
Author(s):  
J.K. Chung(J.K. Jong) ◽  
Pl. Kannappan ◽  
C.T. Ng
Keyword(s):  
Functional Equation ◽  
Sine Functional Equation

A sine functional equation

1969 ◽  
Vol 2 (2-3) ◽  
pp. 397-398
Author(s):  
J. A. Baker
Keyword(s):  
Functional Equation ◽  
Sine Functional Equation

The Cosine–Sine functional equation on a semigroup with an involutive automorphism

2017 ◽  
Vol 91 (6) ◽  
pp. 1115-1146 ◽  
Author(s):  
Omar Ajebbar ◽  
Elhoucien Elqorachi
Keyword(s):  
Functional Equation ◽  
Involutive Automorphism ◽  
Sine Functional Equation
Sign in / Sign up

Export Citation Format

Share Document