• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.225-234
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• 2023

In this paper, we use the use the linear operator ʒ^x_τ,σ(u, v, y)𝔣(z) and the concept of the subordination to analyse the general class of all analytic univalent functions. Our main results are implication properties between the classes of such functions and the application of these properties to special cases.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.393-401
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• 2007

In the present paper we introduce the subclass $S^{\lambda}_{a,c}(p,A,B)$ of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5].

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.773-784
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• 2022

The purpose of the present paper is to estimate some real parts for certain analytic functions with some applications in connection with certain integral operators and geometric properties. Also we extend some known results as special cases of main results presented here.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.459-465
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• 2013

Let $p(z)$ be an analytic function defined on the open unit disk D and $p(0)=1$. Condition ${\beta}$ in terms of complex numbers D and real E with -1 < E < 1 and ${\mid}D{\mid}{\leq}1$ is determined such that $1+{\beta}{\prec}\frac{1+Dz}{1+Ez}$ implies $p(z){\prec}\sqrt{1+z}$. Furthermore, the expression $1+\frac{{\beta}zp^{\prime}(z)}{p(z)}$ and $1+\frac{{\beta}zp^{\prime}(z)}{p^2(z)}$ are considered in obtaining similar results.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.115-126
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• 1995

Let A be the class of univalent functions f(z)=z＋${\alpha}$$_2$z$^2$＋${\alpha}$$_3$z$^3$＋…(1.1) which are analytic in the unit disk $\Delta$= {z：│z│＜1}. Let S＊(p) be the subclass of A composing of functions which are starlike of order $\rho$. A function f(z) belonging to the class A is said to be starlike of order $\rho$ ($\rho$(equation omitted) 0) if and only if z$\^$-l/ f(z) (equation omitted) 0 (z$\in$$\Delta$) and (equation omitted (1.2).(omitted)

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1287-1298
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• 2020

Inspired by a classical approximation result of Bagemihl and Seidel on the disc, we provide generalized results on some proper domains in ℂⁿ about approximation of a continuous function by a holomorphic function in the Mergelyan's style.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.905-915
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• 2009

Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.141-151
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• 2022

The purpose of the present paper is to obtain some conditions for strongly starlikeness and univalence of normalized analytic functions in the open unit disk. Further, we prove an univalence and argument properties for certain integral operators.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.259-267
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• 2023

The paper presents the introduction of a novel linear derivative operator for meromorphic functions that are linked with q-calculus. Using the linear derivative operator, a new category of meromorphic functions is generated in the paper. We obtain sufficient conditions and show some properties of functions belonging to these subclasses. The partial sums of its sequence and the q-neighborhoods problem are solved.