Results 271 to 280 of about 53,868 (294)

On a characteristic of cosine functions

Semigroup Forum, 2013
In this note, the notion of strongly continuous cosine function in a Banach space is investigated by using the Laplace transform, and some results are given. It is well known that this operator-valued function is the solution operator (i.e., propagator) for a well-posed incomplete second order abstract Cauchy problem in a Banach space.
Mei, Zhan-Dong, Peng, Ji-Gen, Zhang, Yang   +2 more
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A Functional Equation for the Cosine

Canadian Mathematical Bulletin, 1968
It is known [3], [5] that, the complex-valued solutions of(B)(apart from the trivial solution f(x)≡0) are of the form(C)(D)In case f is a measurable solution of (B), then f is continuous [2], [3] and the corresponding ϕ in (C) is also continuous and ϕ is of the form [1],(E)In this paper, the functional equation(P)where f is a complex-valued, measurable
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On the cosine-sine functional equation on groups

aequationes mathematicae, 2002
The authors find the solutions \(f,g\in C(G)\) of each of the functional equations \[ \frac{f(x+y)\pm f(x+\sigma y)}{2}=f(x)g(y)+g(x)f(y)+h(x)h(y), \;\forall x,y\in G \] where \(G\) is a topological Abelian group, \(\sigma :G\longrightarrow G\) is a continuous involutive automorphism of \(G\), and where \(C(G)\) denotes the algebra of continuous ...
Friis, P. de Place, Stetkær, H.
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Evaluating the Cosine Function

The Mathematics Teacher, 1971
The cosine function is a mapping of real numbers into real numbers. The function is called cos, and the mapping is usually described with reference to a geometric figure that involves a number circle and a number line. (See fig. 1.)
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Application of the cosine function

The Mathematics Teacher, 1963
A project for the trigonometry ...
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On an exponential-cosine functional equation

Periodica Mathematica Hungarica, 1988
Let X be a Banach space, \({\mathbb{C}}\) the complex numbers, and let f: \(X\to {\mathbb{C}}\) satisfy the functional equation \((A)\quad f(x+y)+(2f^ 2(y)- f(2y))f(x-y)=2f(x)f(y).\) (A) generalizes the well-studied equations of D'Alembert and Cauchy: \((D)\quad F(x+y)+F(x-y)=2F(x)F(y),\) and \((C)\quad G(x+y)=G(x)G(y),\) respectively.
Parnami, J. C., Singh, H., Vasudeva, H. L.   +2 more
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On the Cosine Functional Equation

1968
Application of functional equations has preceded the development of a systematic theory of functional equations. One of the important applications of functional equations is a functional characterization of various functions like Euler’s Γ function, Lebesgue’s singular function, cyclic functions, polynomials, exponential and logarithmic functions, etc.
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A Cosine Functional Equation in Hilbert Space

Canadian Journal of Mathematics, 1960
Throughout this paper R denotes the set of all real numbers, m(K) the Lebesgue measure of K ⊆ R, H a Hilbert space, L(H) the set of all linear continuous mappings of H into H, endowed with the usual structure of a Banach space.We consider the mapping F of the set R into L(H) such thatholds for all x, y ∈ R. In (2) we have solved this equation under the
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A Cosine Functional Equation with Restricted Argument

Canadian Mathematical Bulletin, 1974
We name a functional equation with restricted argument one in which at least one of the variables is restricted to a certain discrete subset of the domain of the other variable(s). In particular, the subset may consist of a single element.The purpose of this paper is to present a functional equation satisfied only by cosine functions.
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Discrete Approximations of Cosine Operator Functions. I

SIAM Journal on Numerical Analysis, 1982
Summary: We are concerned with the approximation of cosine operator functions which appear in a natural way in the study of the Cauchy problem for second order evolution equations. We derive both qualitative and quantitative convergence theorems characterizing the convergence of cosine operator functions in terms of their infinitesimal generators, and ...
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