• Honam Mathematical Journal
• /
• v.42 no.4
• /
• pp.719-731
• /
• 2020

In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.465-481
• /
• 2021

Let f be the function defined on the open unit disk, with f(0) = 0 = f'(0) - 1, satisfying Re (αf'(z) + (1 - α)zf'(z)/f(z)) > 0 or Re (αf'(z) + (1 - α)(1 + zf"(z)/f'(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.331-347
• /
• 2017

The aim of the present paper is to introduce a new subclass of meromorphic functions with positive coefficients defined by a certain integral operator and a necessary and sufficient condition for a function f to be in this class. We obtain coefficient inequality, meromorphically radii of close-to-convexity, starlikeness and convexity, convex linear combinations, Hadamard product and integral transformation for the functions f in this class.

• Honam Mathematical Journal
• /
• v.37 no.3
• /
• pp.317-323
• /
• 2015

The purpose of the present paper is to study certain radii problems for the function $$f(z)=\[{\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}\(z^{\gamma}[D^nF(z)]^{\beta}\)^{\prime}\]^{1/{\beta}}$$, where ${\beta}$ is a positive real number, ${\gamma}$ is a complex number such that ${\gamma}+{\beta}{\neq}0$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.445-454
• /
• 2022

Using the concept of the strong differential subordination introduced in [2], we find conditions on the functions θ, 𝜑, G, F such that the first order strong subordination θ(p(z)) + $\frac{G(\xi)}{\xi}$zp'(z)𝜑(p(z)) ≺≺ θ(q(z)) + F(z)q'(z)𝜑(q(z), implies p(z) ≺ q(z), where p(z), q(z) are analytic functions in the open unit disk 𝔻 with p(0) = q(0). Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in [1].

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.659-666
• /
• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1139-1148
• /
• 2015

The estimate of third Hankel determinant $$H_{3,1}(f)=\left|a_1\;a_2\;a_3\\a_2\;a_3\;a_4\\a_3\;a_4\;a_5\right|$$ of the analytic function $f(z)=z+a2z^2+a3z^3+{\cdots}$, for which ${\Re}(1+zf^{{\prime}{\prime}}(z)/f^{\prime}(z))>-1/2$ are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.445-458
• /
• 2018

In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. Some open problems with this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.

• Journal of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1147-1180
• /
• 2021

By considering the polynomial function 𝜙_car(z) = 1 + z + z²/2, we define the class 𝓢^*_car consisting of normalized analytic functions f such that zf'/f is subordinate to 𝜙_car in the unit disk. The inclusion relations and various radii constants associated with the class 𝓢^*_car and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.12C
• /
• pp.1194-1200
• /
• 2006

In this paper, we propose an adaptive MAP (Maximum A Posteriori) high-resolution image reconstruction algorithm using local statistics. In order to preserve the edge information of an original high-resolution image, a visibility function defined by local statistics of the low-resolution image is incorporated into MAP estimation process, so that the local smoothness is adaptively controlled. The weighted non-quadratic convex functional is defined to obtain the optimal solution that is as close as possible to the original high-resolution image. An iterative algorithm is utilized for obtaining the solution, and the smoothing parameter is updated at each iteration step from the partially reconstructed high-resolution image is required. Experimental results demonstrate the capability of the proposed algorithm.