In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14...In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.展开更多
In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where...In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.展开更多
文摘In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.
文摘In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.
