• Title, Summary, Keyword: Analytic Inequalities

Search Result 39, Processing Time 0.038 seconds

FEKETE-SZEGÖ PROBLEM FOR SUBCLASSES OF STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS

  • Shanmugam, T.N.;Ramachandram, C.;Ravichandran, V.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.43 no.3
    • /
    • pp.589-598
    • /
    • 2006
  • In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

Priority Setting for the Healthy City Program in Busan Using the Analytic Hierarchy Process (계층 분석법을 적용한 부산시 건강도시 사업의 우선순위 설정)

  • Yoon, Tae-Ho;Choi, Min-Hyeok;Cheong, Kyu-Seok;Kim, Yun-Hee;Kim, Keon-Yeop;Jung, Baek-Geun
    • Korean Journal of Health Education and Promotion
    • /
    • v.28 no.3
    • /
    • pp.31-42
    • /
    • 2011
  • Objectives: Busan had the highest mortality and the shortest life expectancy at birth among 16 provinces in Korea in 2008 and there were considerable health inequalities within the region. This study was performed to build up a priority setting framework in Healthy City Busan project. Methods: Analytic hierarchy process was used to determine the relative priority weight for different strategic and program dimensions along with the consistency of response. An on-site workshop-based meeting (calculating importance) and online survey (calculating risk) were conducted to obtain data from 8 experts. Results: The results showed that in strategic criteria "active health promotion & diseases prevention" and "building infrastructure for the Health City project" were two most important factors. In program criteria, considering both importance and risk scores, "making a healthy community" and "building community health centers" in disadvantaged areas were a top priority group. In addition, "enacting an ordinance for the Healthy City", "building the infrastructure for health impact assessment" and "making health care safety net for vulnerable population" were also higher priorities group. Conclusions: Our findings suggest that the Healthy City project in Busan should be focused on strengthening health equity and building infrastructure for sustainability of the project.

On a Class of Spirallike Functions associated with a Fractional Calculus Operator

  • SELVAKUMARAN, KUPPATHAI APPASAMY;BALACHANDAR, GEETHA;RAJAGURU, PUGAZHENTHI
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.4
    • /
    • pp.953-967
    • /
    • 2015
  • In this article, by making use of a linear multiplier fractional differential operator $D^{{\delta},m}_{\lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-$Szeg{\ddot{o}}$ inequalities.

Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities

  • MENDIRATTA, RAJNI;NAGPAL, SUMIT;RAVICHANDRAN, V.
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.2
    • /
    • pp.395-410
    • /
    • 2015
  • For functions $f(z)=z+a_2z^2+a_3z^3+{\cdots}$ with ${\mid}a_2{\mid}=2b$, $b{\geq}0$, sharp radii of starlikeness of order ${\alpha}(0{\leq}{\alpha}<1)$, convexity of order ${\alpha}(0{\leq}{\alpha}<1)$, parabolic starlikeness and uniform convexity are derived when ${\mid}a_n{\mid}{\leq}M/n^2$ or ${\mid}a_n{\mid}{\leq}Mn^2$ (M>0). Radii constants in other instances are also obtained.

On the Fekete-Szegö Problem for a Certain Class of Meromorphic Functions Using q-Derivative Operator

  • Aouf, Mohamed Kamal;Orhan, Halit
    • Kyungpook Mathematical Journal
    • /
    • v.58 no.2
    • /
    • pp.307-318
    • /
    • 2018
  • In this paper, we obtain $Fekete-Szeg{\ddot{o}}$ inequalities for certain class of meromorphic functions f(z) for which $-{\frac{(1-{\frac{{\alpha}}{q}})qzD_qf(z)+{\alpha}qzD_q[zD_qf(z)]}{(1-{\frac{{\alpha}}{q}})f(z)+{\alpha}zD_qf(z)}{\prec}{\varphi}(z)$(${\alpha}{\in}{\mathbb{C}}{\backslash}(0,1]$, 0 < q < 1). Sharp bounds for the $Fekete-Szeg{\ddot{o}}$ functional ${\mid}{\alpha}_1-{\mu}{\alpha}^2_0{\mid}$ are obtained.

HOLOMORPHIC FUNCTIONS ON THE MIXED NORM SPACES ON THE POLYDISC

  • Stevic, Stevo
    • Journal of the Korean Mathematical Society
    • /
    • v.45 no.1
    • /
    • pp.63-78
    • /
    • 2008
  • We generalize several integral inequalities for analytic functions on the open unit polydisc $U^n={\{}z{\in}C^n||zj|<1,\;j=1,...,n{\}}$. It is shown that if a holomorphic function on $U^n$ belongs to the mixed norm space $A_{\vec{\omega}}^{p,q}(U^n)$, where ${\omega}_j(\cdot)$,j=1,...,n, are admissible weights, then all weighted derivations of order $|k|$ (with positive orders of derivations) belong to a related mixed norm space. The converse of the result is proved when, p, q ${\in}\;[1,\;{\infty})$ and when the order is equal to one. The equivalence of these conditions is given for all p, q ${\in}\;(0,\;{\infty})$ if ${\omega}_j(z_j)=(1-|z_j|^2)^{{\alpha}j},\;{\alpha}_j>-1$, j=1,...,n (the classical weights.) The main results here improve our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577-587 and Z. Anal. Anwendungen 23 (2004), no. 4, 775-782.

ON THE FEKETE-SZEGO PROBLEM FOR CERTAIN ANALYTIC FUNCTIONS

  • Kwon, Oh-Sang;Cho, Nak-Eun
    • The Pure and Applied Mathematics
    • /
    • v.10 no.4
    • /
    • pp.265-271
    • /
    • 2003
  • Let $CS_\alpha(\beta)$ denote the class of normalized strongly $\alpha$-close-to-convex functions of order $\beta$, defined in the open unit disk $\cal{U}$ of $\mathbb{C}$${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$ such that $g\; \in\;S^{\ask}$, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to $CS_\alpha(\beta)$.

  • PDF

A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION

  • Ali Rosihan M.;Khan M. Hussain;Ravichandran V.;Subramanian K.G.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.43 no.1
    • /
    • pp.179-188
    • /
    • 2006
  • For a given p-valent analytic function g with positive coefficients in the open unit disk $\Delta$, we study a class of functions $f(z) = z^p - \sum\limits{_{n=m}}{^\infty} a_nz^n(a_n{\geq}0)$ satisfying $$\frac 1 {p}{\Re}\;(\frac {z(f*g)'(z)} {(f*g)(z)})\;>\;\alpha\;(0{\leq}\;\alpha\;<\;1;z{\in}{\Delta})$$ Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.

Reconfiguration Control Using LMI-based Constrained MPC (선형행렬부등식 기반의 모델예측 제어기법을 이용한 재형상 제어)

  • Oh, Hyon-Dong;Min, Byoung-Mun;Kim, Tae-Hun;Tahk, Min-Jea;Lee, Jang-Ho;Kim, Eung-Tai
    • Journal of the Korean Society for Aeronautical & Space Sciences
    • /
    • v.38 no.1
    • /
    • pp.35-41
    • /
    • 2010
  • In developing modern aircraft, the reconfiguration control that can improve the safety and the survivability against the unexpected failure by partitioning control surfaces into several parts has been actively studied. This paper deals with the reconfiguration control using model predictive control method considering the saturation of control surfaces under the control surface failure. Linearized aircraft model at trim condition is used as the internal model of model predictive control. We propose the controller that performs optimization using LMI (linear matrix inequalities) based semi-definite programming in case that control surface saturation occurs, otherwise, uses analytic solution of the model predictive control. The performance of the proposed control method is evaluated by nonlinear simulation under the flight scenario of control surface failure.