The main results will be proved by employing Hlder's inequality, Minkowski's inequality and a chain rule on time scales. As special cases of our results, when the time scale is the real numbers, we will derive some well-known results due to Copson, Bliss, Flett and Bennett by a ...
InequalityforMarcinkiewicz——Fej6r ConjugateWalsh——FourierSeries UshangiGOGINAVA InstituteofMathematics,FacultyofExactandNaturalSciences,TbilisiStateUniversity, Chavchavadzestr.1,Tbilisi0128,Georgia E-mail:z_goginava@hotmail.COrn Abstract Themainaimofthispaperistoprovethatforany0 ...
In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.doi:10.4153/CJM-2010-033-9Yongyang JinGenkai ZhangmathematicsY. Jin and G. Zhang, "Degenerate p-Laplacian operators on H-type groups ...
Hardy-type inequality for fuzzy integrals In [10], Hardy proved the following inequality:∫0∞Fxpdx<pp-1p∫0∞fp(x)dx,where p>1, f:[0,∞)→[0,∞) is an integrable function (f≠0) and F(x)=∫0xf(t)dt. Furthermore, for parameters a,b such that 0<a<b<∞, the following in...
1) Hardy type inequality Hardy型不等式 1. TheHardy type inequalityis extended to the Banach-space-valued Vilenkin martingales-Fourier coefficients. 对Banach空间值Vilenkin鞅建立了Hardy型不等式,推广了Weisz中的相应结论。 2. A class ofHardy type inequalityis given by the method of function representatio...
Hardy-type inequality with double singular kernelsand the constantγ= (βp−1)/p. Note thatγ >0andk≥−1. Lets(x) =|x|/λ(x), consider the nonnegative kernelsv(x) =|x|1−α|g(s(x))|1−β;w(x) =|x|−α|g(s(x))|−β:(2)The functionv(resp.w) is singular...
Hölder’s inequalityFubini theoremweight functionIn this paper, we give some new generalizations to the Hardy-type integral inequalities for functions of two variables by using weighted mean operators \\(S_{1}:=S_{1}^{w}f\\) and \\(S_{2}:=S_{2}^{w}f\\) defined by $$\\begin...
It states that inequality is showed for the intervals (0, R) and (R, +∞) separately through the Hölder inequality and the aid of integration by parts. It says that inequalities can be demonstrated in a factorization form over weighted analogues and a set of constraints of the Poincaré ...
In the second section, the non-linear case (a general Hardy-type inequality) is handled with a direct and analytic proof. In the last section, it is illustrated that the basic estimates presented in the first two sections can still be improved considerably. 展开 ...
摘要: In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that 关键词: Theoretical or Mathematical/ fuzzy set theory integral equations/ Jensen type inequality fuzzy integrals Sugeno integral fuzzy measures/ C1160 Combinatorial mathematics C4180 Integral ...