• 대한수학회논문집
• /
• 제37권4호
• /
• pp.1025-1039
• /
• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Korean Journal of Mathematics
• /
• 제25권3호
• /
• pp.389-403
• /
• 2017

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with respect to k-symmetric points. We also study certain interesting properties like covering theorem, convolution condition, neighborhood results and argument theorem.

• Kyungpook Mathematical Journal
• /
• 제59권3호
• /
• pp.493-503
• /
• 2019

In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients ${\mid}a_{m+1}{\mid}$ and ${\mid}a_{2m+1}{\mid}$. Also, we indicate certain special cases for our results.

• 대한수학회보
• /
• 제51권4호
• /
• pp.1229-1240
• /
• 2014

In this paper we provide three results involving large Schr$\ddot{o}$der paths. First, we enumerate the number of large Schr$\ddot{o}$der paths by type. Second, we prove that these numbers are the coefficients of a certain symmetric function defined on the staircase skew shape when expanded in elementary symmetric functions. Finally we define a symmetric function on a Fuss path associated with its low valleys and prove that when expanded in elementary symmetric functions the indices are running over the types of all Schr$\ddot{o}$der paths. These results extend their counterparts of Kreweras and Armstrong-Eu on Dyck paths respectively.

• 정보보호학회논문지
• /
• 제19권2호
• /
• pp.23-30
• /
• 2009

회전대칭 불함수는 고속계산에 유리하고 암호학적으로 우수한 성질을 나타내어 최근 많은 주목을 받고 있다. 예를 들어, 부호이론에서 중요한 문제가 회전대칭 불함수를 이용하여 해결된 사례가 있고, 고속 해시함수 설계에 응용된 경우도 있다. 다른 한편으로, 매우 단순한 형태의 회전대칭 이차 불함수에 대한 비선형성 및 해명무게의 정확한 공식이 발견되었으며[2,8], 더 넓은 범위의 함수들에 대한 보다 일반적인 공식들도 발견되었다[6]. 본 논문에서는 이들 공식들을 조금 더 확장하여 일차항들이 포함된 회전대칭 이차 불함수에 대한 정확한 해밍무게 공식을 유도한다.

• 대한수학회논문집
• /
• 제28권1호
• /
• pp.143-154
• /
• 2013

We introduce a subclass $S_s^{({\kappa})}$(A,B) (-1 ${\leq}$ B < A ${\leq}$ 1) of functions which are analytic in the open unit disk and close-to-convex with respect to ${\kappa}$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.

• Journal of applied mathematics & informatics
• /
• 제40권1_2호
• /
• pp.243-257
• /
• 2022

In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.

• 호남수학학술지
• /
• 제40권4호
• /
• pp.733-748
• /
• 2018

In this paper, we investigate a new subclass $S^{{\varphi},{\lambda}}_{{\Sigma}_m}$ of ${\Sigma}_m$ consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-$Szeg{\ddot{o}}$ inequalities for this class. Also, we establish estimates for the coefficients for this subclass and several related classes are also considered and connections to earlier known results are made.

• 대한수학회논문집
• /
• 제37권2호
• /
• pp.455-472
• /
• 2022

For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST_[j,k](A, B) and K_[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a²₃ - a₅|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST_[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K_[j,k](α) for all 0 ≤ α < 1.

• Journal of applied mathematics & informatics
• /
• 제34권1_2호
• /
• pp.107-114
• /
• 2016

In this paper we give some symmetric property of the generalized twisted q-Euler zeta functions and q-Euler polynomials.