• 제목/요약/키워드: sharp bounds

검색결과 47건 처리시간 0.019초

A Sharp Cramer-Rao type Lower-Bound for Median-Unbiased Estimators

  • So, Beong-Soo
    • Journal of the Korean Statistical Society
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    • 제23권1호
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    • pp.187-198
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    • 1994
  • We derive a new Cramer-Rao type lower bound for the reciprocal of the density height of the median-unbiased estimators which improves most of the previous lower bounds and is attainable under much weaker conditions. We also identify useful necessary and sufficient condition for the attainability of the lower bound which is considerably weaker than those for the mean-unbiased estimators. It is shown that these lower bounds are attained not only for the family of continuous distributions with monotone likelihood ratio (MLR) property but also for the location and scale families with strong unimodal property.

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THIRD HANKEL DETERMINANTS FOR STARLIKE AND CONVEX FUNCTIONS OF ORDER ALPHA

  • Orhan, Halit;Zaprawa, Pawel
    • 대한수학회보
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    • 제55권1호
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    • pp.165-173
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    • 2018
  • In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY

  • Ornek, Bulent Nafi
    • 대한수학회논문집
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    • 제31권3호
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    • pp.533-547
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    • 2016
  • In this paper, a generalized boundary version of $Carath{\acute{e}}odory^{\prime}s$ inequality for holomorphic function satisfying $f(z)= f(0)+a_pz^p+{\cdots}$, and ${\Re}f(z){\leq}A$ for ${\mid}z{\mid}$<1 is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime}(c)$ at the point c with ${\Re}f(c)=A$. The sharpness of these estimates is also proved.

Sharp Coefficient Bounds for the Quotient of Analytic Functions

  • Park, Ji Hyang;Kumar, Virendra;Cho, Nak Eun
    • Kyungpook Mathematical Journal
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    • 제58권2호
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    • pp.231-242
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    • 2018
  • We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

SHARP ESTIMATES ON THE THIRD ORDER HERMITIAN-TOEPLITZ DETERMINANT FOR SAKAGUCHI CLASSES

  • Kumar, Sushil;Kumar, Virendra
    • 대한수학회논문집
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    • 제37권4호
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    • pp.1041-1053
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    • 2022
  • In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.

SHARP BOUNDS OF FIFTH COEFFICIENT AND HERMITIAN-TOEPLITZ DETERMINANTS FOR SAKAGUCHI CLASSES

  • Surya Giri;S. Sivaprasad Kumar
    • 대한수학회보
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    • 제61권2호
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    • pp.317-333
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    • 2024
  • For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S*s(𝜑) and Cs(𝜑), respectively, the sharp bound of the nth Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

ON A CERTAIN CLASS OF p-VALENT UNIFORMLY CONVEX FUNCTIONS USING DIFFERENTIAL OPERATOR

  • Lee, S.K.;Khairnar, S.M.;Rajas, S.M.
    • Korean Journal of Mathematics
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    • 제19권1호
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    • pp.1-16
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    • 2011
  • In this paper, using differential operator, we have introduce new class of p-valent uniformly convex functions in the unit disc U = {z : |z| < 1} and obtain the coefficient bounds, extreme bounds and radius of starlikeness for the functions belonging to this generalized class. Furthermore, partial sums $f_k(z)$ of functions $f(z)$ in the class $S^*({\lambda},{\alpha},{\beta})$ are considered. The various results obtained in this paper are sharp.

DOMINATION IN DIGRAPHS

  • Lee, Chang-Woo
    • 대한수학회지
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    • 제35권4호
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    • pp.843-853
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    • 1998
  • We establish bounds for the domination number of a digraph in terms of the minimum indegree and the order, and then we find a sharp upper bound for the domination number of a weak digraph with minimum indegree one. We also determine the domination number of a random digraph.

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UNIVALENT HARMONIC EXTERIOR MAPPINGS

  • Jun, Sook Heui
    • 충청수학회지
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    • 제16권2호
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    • pp.31-41
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    • 2003
  • In this paper, we will show that the bounds for coefficients of harmonic, orientation-preserving, univalent mappings f defined on ${\Delta}$ = {z : |z| > 1} with $f({\Delta})={\Delta}$ are sharp by finding extremal functions.

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