Binomial andQ-Binomial Coefficient Inequalities Related to the Hamiltonicity of the Kneser Graphs and TheirQ-Analogues

AbstractIn this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions.

Download Full-text

Short proof that Kneser graphs are Hamiltonian for n ⩾ 4k

Discrete Mathematics ◽

10.1016/j.disc.2021.112430 ◽

2021 ◽

Vol 344 (7) ◽

pp. 112430

Author(s):

Johann Bellmann ◽

Bjarne Schülke

Keyword(s):

Short Proof ◽

Kneser Graphs

Download Full-text

An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

Mathematica Slovaca ◽

10.1515/ms-2017-0374 ◽

2020 ◽

Vol 70 (3) ◽

pp. 599-604

Author(s):

Şahsene Altinkaya

Keyword(s):

Error Function ◽

Trigonometric Polynomials ◽

Error Functions ◽

The Family ◽

Coefficient Inequalities

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

Download Full-text

On the neighborhood complex of s→-stable Kneser graphs

Discrete Mathematics ◽

10.1016/j.disc.2021.112302 ◽

2021 ◽

Vol 344 (4) ◽

pp. 112302

Author(s):

Hamid Reza Daneshpajouh ◽

József Osztényi

Keyword(s):

Neighborhood Complex ◽

Kneser Graphs

Download Full-text

Coefficient inequalities for a subclass of Bazilevič functions

Demonstratio Mathematica ◽

10.1515/dema-2020-0040 ◽

2020 ◽

Vol 53 (1) ◽

pp. 27-37

Author(s):

Sa’adatul Fitri ◽

Derek K. Thomas ◽

Ratno Bagus Edy Wibowo ◽

Keyword(s):

Recent Work ◽

Sharp Bounds ◽

Coefficient Problems ◽

Coefficient Inequalities ◽

Bazilevic Functions

AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying \left|f^{\prime} (z){\left(\frac{z}{f(z)}\right)}^{1-\alpha }-1\right|\lt \lambda for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f\in { {\mathcal B} }_{1}(\alpha ,\lambda ), thus extending recent work in the case λ = 1.

Download Full-text

A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

Journal of Function Spaces ◽

10.1155/2017/9010964 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7

Author(s):

Saqib Hussain ◽

Akhter Rasheed ◽

Muhammad Asad Zaighum ◽

Maslina Darus

Keyword(s):

Convolution Operator ◽

Starlike Functions ◽

Distortion Theorem ◽

Open Unit ◽

Uniformly Convex ◽

Open Unit Disc ◽

Coefficient Inequalities ◽

Uniformly Starlike Functions ◽

Convex And Starlike Functions ◽

Uniformly Starlike

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.

Download Full-text

On the Prague Dimension of Kneser Graphs

Numbers, Information and Complexity ◽

10.1007/978-1-4757-6048-4_12 ◽

2000 ◽

pp. 125-128 ◽

Cited By ~ 2

Author(s):

Zoltán Füredi

Keyword(s):

Kneser Graphs

Download Full-text

Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v37i4.32701 ◽

2018 ◽

Vol 37 (4) ◽

pp. 83-95

Author(s):

Trailokya Panigrahi ◽

Janusz Sokól

Keyword(s):

Upper Bound ◽

Analytic Functions ◽

Hankel Determinant ◽

Lemniscate Of Bernoulli ◽

Toeplitz Determinant ◽

Second Hankel Determinant ◽

Coefficient Inequalities ◽

The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*} associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}| for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

Download Full-text