http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
MEAN-VALUE PROPERTY AND CHARACTERIZATIONS OF SOME ELEMENTARY FUNCTIONS
Matkowski, Janusz Korean Mathematical Society 2013 대한수학회보 Vol.50 No.1
A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.
Mean-value property and characterizations of some elementary functions
Janusz Matkowski 대한수학회 2013 대한수학회보 Vol.50 No.1
Abstract. A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation [수식] where M is a given mean and f, F, g,G are the unknown functions. Solv- ing this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homo- graphic and square-root functions. A new criterion of the monotonicity of a real function is presented.
Glazowska, Dorota,Guerrero, Jose Atilio,Matkowski, Janusz,Merentes, Nelson Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.
Dorota G lazowska,Jos\'e Atilio Guerrero,Janusz Matkowski,Nelson Merentes 대한수학회 2013 대한수학회보 Vol.50 No.2
We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.