## Displaying similar documents to “Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points”

### Uniformly convex functions II

Annales Polonici Mathematici

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses ${f}^{-1}\left(w\right)=w+d₂w²+d₃w³+...$. The series expansion for ${f}^{-1}\left(w\right)$ converges when $|w|<{\varrho }_{f}$, where $0<{\varrho }_{f}$ depends on f. The sharp bounds on $|{a}_{n}|$ and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on $|{a}_{n}|$ and all extremal functions for...

### Some subclasses of close-to-convex functions

Annales Polonici Mathematici

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For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes ${C}_{\beta }\left(\alpha \right)$ defined as follows: a function f regular in U = z: |z| < 1 of the form $f\left(z\right)=z+{\sum }_{n=1}^{\infty }{a}_{n}{z}^{n}$, z ∈ U, belongs to the class ${C}_{\beta }\left(\alpha \right)$ if $Re{e}^{i\beta }\left(1-\alpha ²z²\right){f}^{\text{'}}\left(z\right)<0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in ${C}_{\beta }\left(\alpha \right)$ are examined.

### Argument estimates of certain multivalent functions involving Dziok-Srivastava operator.

General Mathematics

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### Applications of Nunokawa's theorem.

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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### Inequalities in the complex plane.

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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### On potentially $H$-graphic sequences

Czechoslovak Mathematical Journal

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For given a graph $H$, a graphic sequence $\pi =\left({d}_{1},{d}_{2},...,{d}_{n}\right)$ is said to be potentially $H$-graphic if there is a realization of $\pi$ containing $H$ as a subgraph. In this paper, we characterize the potentially $\left({K}_{5}-e\right)$-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence $\pi$ to be potentially ${K}_{5}$-graphic, where ${K}_{r}$ is a complete graph on $r$ vertices and ${K}_{r}-e$ is a graph obtained from ${K}_{r}$ by deleting one edge. Moreover, we also give a simple necessary and sufficient condition...

### A remark on supra-additive and supra-multiplicative operators on $C\left(X\right)$

Mathematica Bohemica

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M. Radulescu proved the following result: Let $X$ be a compact Hausdorff topological space and $\pi \phantom{\rule{0.222222em}{0ex}}C\left(X\right)\to C\left(X\right)$ a supra-additive and supra-multiplicative operator. Then $\pi$ is linear and multiplicative. We generalize this result to arbitrary topological spaces.

### On potentially ${K}_{5}-H$-graphic sequences

Czechoslovak Mathematical Journal

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Let ${K}_{m}-H$ be the graph obtained from ${K}_{m}$ by removing the edges set $E\left(H\right)$ of $H$ where $H$ is a subgraph of ${K}_{m}$. In this paper, we characterize the potentially ${K}_{5}-{P}_{4}$ and ${K}_{5}-{Y}_{4}$-graphic sequences where ${Y}_{4}$ is a tree on 5 vertices and 3 leaves.