• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.127-145
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• 2009

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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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.

• 호남수학학술지
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• 제46권3호
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• pp.515-521
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• 2024

In our paper, by using different inequalities regarding the coefficients of the normalized close-to-convex functions in the open unit disk, we found a smaller upper bound of the third Hankel determinant for the class of close-to-convex functions as compared with those obtained by Prajapat et. al. in 2015.

• 호남수학학술지
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• 제37권3호
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• pp.317-323
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• 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.

• 호남수학학술지
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• 제9권1호
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• pp.71-76
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• 1987

Let M be a positive real number and c a complex numbcr such that $\left|c-1\right|<M{\leq}Re{c}$. Let $f,f(z)=z+a_{2}Z^{2}+...,$ be analytic and univalent in the unit disc. It is said to belong to the class S(c, M) if $\left|zf'(z)/f(z)-c\right|<M$ We find growth and rotation theorems for the class S(c, M).

• 대한수학회논문집
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• 제37권4호
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• pp.995-1007
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• 2022

In this article, we initiate subclasses of functions with boundary and radius rotations that are related to limaçon domains and examine some of their geometric properties. Radius results associated with functions in these classes and their linear combination are studied. Furthermore, the growth rate of coefficients, arc length and coefficient estimates are derived for these novel classes. Overall, some useful consequences of our findings are also illustrated.

• 호남수학학술지
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• 제42권2호
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• pp.377-389
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• 2020

In this paper, we are mainly interested to find sufficient conditions for the convolution operator 𝓨_λ,µf(z) = zW_λ,µ(z) ∗ f(z) belonging to the classes 𝓤𝓒𝓥 (k, α), 𝓢_p (k, α), S*_ς and C_ς.

• East Asian mathematical journal
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• 제4권
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• pp.57-73
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• 1988

The subclasses S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) ($0\leqq\alpha<1,\;0<\beta\leqq1$ and $0\leqq\mu\leqq1$) of T the class of analytic and univalent functions of the form $$f(z)=z-\sum\limit^{\infty}_{n=2}\mid a_n\mid z^n$$ have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) are determined along with a representation formula for the functions in S*($\alpha,\beta,\mu$). Furthermore, it is shown that the classes S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) are closed under arithmetic mean and convex linear combinations. Also in this paper, we find extreme points and support points for these classes.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.259-266
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• 2022

The present investigation is concerned with certain subclasses of alpha-convex functions with fixed point and defined with subordination in the unit disc E = {z :| z |< 1}. The estimates of the first four coefficients for the functions in these classes are obtained. The results due to various authors follow as special cases.