35 research outputs found

    Certain subclasses of multivalent functions defined by new multiplier transformations

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    In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions is defined. Making use of the operator Jpδ(λ,μ,l),\mathrm{% {\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l), two new subclasses Pλ,μ,lδ(A,B;σ,p)\mathcal{% P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p) and P~λ,μ,lδ(A,B;σ,p)\widetilde{\mathcal{P}}% _{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses Pλ,μ,lδ(A,B;σ,p)\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p) and P~λ,μ,lδ(A,B;σ,p)\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p) are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out

    Geometrical Theory of Analytic Functions

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    The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria

    Differential subordination and superordination studies involving symmetric functions using a q-analogue multiplier operator

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    The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the q q -Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided

    Some Properties of Bazilevič Functions Involving Srivastava–Tomovski Operator

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    We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and Fekete–Szegö functional for functions belonging to the class

    New Developments in Geometric Function Theory

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    The book contains papers published in a Special Issue of Axioms, entitled "New Developments in Geometric Function Theory". An Editorial describes the 14 papers devoted to the study of complex-valued functions which present new outcomes related to special classes of univalent and bi-univalent functions, new operators and special functions associated with differential subordination and superordination theories, fractional calculus, and certain applications in geometric function theory
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