• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.357-367
• /
• 2001

Let $Q(\beta)$ be the class of normalized strongly quasiconvex functions of order $\beta$ in the open unit disk. Sharp Fekete-Szego inequalities are obtained for functions belonging to the class $Q(\beta)$. We also consider the integral preserving properties in a sector.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.723-734
• /
• 2022

In this work, we introduce a new subclass of analytic functions of complex order involving the (p, q)-derivative operator defined in the open unit disc. For this class, several Fekete-Szegö type coefficient inequalities are derived. We obtain the results of Srivastava et al. [22] as consequences of the main theorem in this study.

• 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 $CS_\alpha(\beta)$.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.503-511
• /
• 2021

In this present work, we obtain certain coefficients of the subclass 𝓗_λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1035-1041
• /
• 2022

Herein, we construct a qualitative subclass B^γ(κ, µ, σ) of the class of analytic bi-univalent functions. Next, we explore estimates of the coefficients |a_j| (j = 1, 2) and the Fekete-Szegö functional |a₃ - ςa²₂| for functions in this subclass.

• 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.

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.521-534
• /
• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• Communications of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.461-470
• /
• 2024

In this paper, a new subclass, 𝒮𝒞^𝜇,p,q_𝜎 (r, s; x), of Sakaguchitype analytic bi-univalent functions defined by (p, q)-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for |a₂| and |a₃| are obtained. Fekete-Szegö inequalities for the class are found. Finally, we give some corollaries.

• The Pure and Applied Mathematics
• /
• v.31 no.2
• /
• pp.201-216
• /
• 2024

The aim of this paper is to study a new and unified class 𝓡^α_Cosh of analytic functions associated with cosine hyperbolic function in the open unit disc E = {z ∈ ℂ : |z| < 1}. Some interesting properties of this class such as initial coefficient bounds, Fekete-Szegö inequality, second Hankel determinant, Zalcman inequality and third Hankel determinant have been established. Furthermore, these results have also been studied for two-fold and three-fold symmetric functions.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.715-727
• /
• 2021

In this paper, we give some results an upper bound of Hankel determinant of H₂(1) for the classes of 𝓝 (𝜶). We get a sharp upper bound for H₂(1) = c₃ - c²₂ for 𝓝 (𝜶) by adding z₁, z₂, …, z_n zeros of f(z) which are different than zero. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained. Finally, the sharpness of the inequalities obtained in the presented theorems are proved.