• 대한수학회논문집
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• 제38권1호
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• pp.163-178
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• 2023

We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function p defined on the unit disc so that the function p is subordinate to the function e^z. These results are applied to find sufficient conditions for the normalised analytic functions f defined on the unit disc to satisfy the subordination zf'(z)/f(z) ≺ e^z.

• East Asian mathematical journal
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• 제25권2호
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• pp.127-140
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• 2009

In this paper a general class of analytic functions involving a convolution structure is introduced. Among the results investigated are the various results depicting useful properties and characteristics of this function class by employing the techniques of differential subordination. Relevances of the main results with some known results are also mentioned briefly.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.223-236
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• 2023

In the present paper, we investigate the subordination and superordination implications for a class of certain nonlinear integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Further, we extend some results given earlier as special cases of the main results presented here.

• East Asian mathematical journal
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• 제28권3호
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• pp.321-332
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• 2012

The purpose of the present paper is to investigate some subordination and superordination preserving properties of certain integral operators de ned on the space of meromorphic functions in the puncture open unit disk. The sandwich-type theorems for these integral operators are also presented.

• 대한수학회보
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• 제53권1호
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• pp.127-138
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• 2016

Differential subordination and superordination preserving properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.257-270
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• 2018

The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between $Carath{\acute{e}}odory$ functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.243-258
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• 2023

A normalized analytic function f defined on the unit disk 𝔻 is starlike of reciprocal order α, 0 ≤ α < 1, if Re(f(z)/(zf'(z))) > α for all z ∈ 𝔻. Such functions are starlike and therefore univalent in 𝔻. Using the well-known Miller-Mocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order α. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f(z)/(zf'(z)) - 1| < 1 - α.

• 호남수학학술지
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• 제46권1호
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• pp.120-135
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• 2024

A normalized analytic function f, defined on the unit disk 𝔻, is starlike of reciprocal order α > 1 if the real part of f(z)/(zf'(z)) is less than α for all z ∈ 𝔻. By utilizing the theory of differential subordination, we establish several sufficient conditions for analytic functions defined on 𝔻 to be starlike of reciprocal order. Additionally, we investigate the conditions under which the function f(z)/(zf'(z)) is subordinate to the function 1 + (α - 1)z. This subordination, in turn, is sufficient for the function f to be starlike of reciprocal order α > 1.

• 호남수학학술지
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• 제40권2호
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• pp.315-323
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• 2018

In this study, firstly we introduce generalized differential and integral operator, also using integral operator two classes are presented. Furthermore, some subordination results involving the Hadamard product (Convolution) for these subclasses of analytic function are proved. A number of consequences of some of these subordination results are also discussed.

• 대한수학회보
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• 제48권3호
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• pp.627-636
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• 2011

In this paper, we obtain some applications of first order differential subordination and superordination results for higher-order derivatives of p-valent functions involving certain linear operator. Some of our results improve and generalize previously known results.