On the Functional Equation for the Sine. Additional Note

Vleck, Edward B. Van

doi:10.2307/1968082

Cited by 13 publications

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“…when G is a not necessarily abelian group and z 0 is a fixed element in the center of G. We refer also to [11] and [12]. Perkins and Sahoo [6] replaced the group inversion by an involution τ : G −→ G and they obtained the abelian, complex-valued solutions of equation…”

Section: 1)mentioning

confidence: 99%

Integral Van Vleck’s and Kannappan’s functional equations on semigroups

Elqorachi

2016

Aequat. Math.

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Abstract. In this paper we study the solutions of the integral Van Vleck's functional equation for the sineand the integral Kannappan's functional equationwhere S is a semigroup, τ is an involution of S and µ is a measure that is linear combinations of point measures (δz i ) i∈I , such that for all i ∈ I, z i is contained in the center of S. We express the solutions of the first equation by means of multiplicative functions on S, and we prove that the solutions of the second equation are closely related to the solutions of the classic d'Alembert's functional equation with involution.

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Section: 1)mentioning

confidence: 99%

Integral Van Vleck’s and Kannappan’s functional equations on semigroups

Elqorachi

2016

Aequat. Math.

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“…In the papers [8,9], Van Vleck studied the continuous solutions f : R → R, f 6 = 0, of the functional equation f (x − y + z 0 ) − f (x + y + z 0 ) = 2f (x)f (y), x,y ∈ R, (1.1) where z 0 > 0 is fixed. We shall in this paper study extensions of (1.1) and related functional equations from R to locally compact groups.…”

Section: Introductionmentioning

confidence: 99%

The generalized Van Vleck's equation on locally compact groups

Fadli

Zeglami

Kabbaj

2017

Proyecciones (Antofagasta)

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“…The present paper is not the first place to treat Van Vleck's functional equation since Van Vleck [14,15]. The solutions f : R → C of his classical functional equation (1) were derived in the textbooks Kannappan [9, Theorem 3.53] and Stetkaer [13,Exercise 9.18].…”

Section: Introductionmentioning

confidence: 99%

“…The American mathematician Van Vleck [14,15] studied around 1910 the continuous solutions f : R → R, f = 0, of the functional equation…”

Section: Introductionmentioning

confidence: 99%