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Properties and Applications of Complex Fractal–Fractional Operators in the Open Unit Disk
Fractal and FractionalA fractal–fractional calculus is presented in term of a generalized gamma function (ℓ−gamma function: Γℓ(.)). The suggested operators are given in the symmetric complex domain (the open unit disk).
Adel A. Attiya +3 more
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On a new linear operator formulated by Airy functions in the open unit disk [PDF]
Advances in Difference Equations, 2021 In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is
Rabha W. Ibrahim, Dumitru Baleanu
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On the characterization properties of certain hypergeometric functions in the open unit disk
Journal of Inequalities and Applications, 2022 Our purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function z 1 F 2 ( a ; b , c ; z ) $z{}_{1}F_{2}(a;b,c;z)$ in the open unit disk.
Deepak Bansal +3 more
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Coefficients Inequalities for the Bi-Univalent Functions Related to q-Babalola Convolution Operator
Fractal and Fractional, 2023 This article defines a new operator called the q-Babalola convolution operator by using quantum calculus and the convolution of normalized analytic functions in the open unit disk.
Isra Al-shbeil +2 more
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MethodsX, 2023 Analytic functions are very helpful in many mathematical and scientific uses, such as complex integration, potential theory, and fluid dynamics, due to their geometric features.
Ibtisam Aldawish, Rabha W. Ibrahim
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Mathematics, 2023 Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for estimating the Taylor–Maclaurin coefficients and the Fekete–Szegö functional.
Abdulmtalb Hussen, Abdelbaset Zeyani
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Characterization of the asymptotic Teichmüller space of the open unit disk through shears [PDF]
Pure and Applied Mathematics Quarterly, 2014 We give a parametrization to the asymptotic Teichmuller space of the open unit disk through equivalent classes of shear functions induced by quasisymmetric homeomorphisms on the Farey tesselation of the unit disk. Then using the parametrization, we define a new metric on the asymptotic Teichmuller space. Two other related metrics are also introduced on
Fan, Jinhua, Hu, Jun
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New classes of spaceable sets of analytic functions on the open unit disk
Colloquium Mathematicum, 2022 In this paper we study an algebraic and topological structure inside the following sets of special functions: Bloch functions defined on the open unit disk that are unbounded and analytic functions of bounded type defined a Banach algebra E into E, which are not Lorch-analytic.
Lourenço, M. Lilian, Vieira, Daniela M.
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New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality
Journal of Mathematics, 2022 In the recent past, various new subclasses of normalized harmonic functions have been defined in open unit disk U which satisfy second-order and third-order differential inequalities.
Mohammad Faisal Khan +4 more
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Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions [PDF]
, 2015 In this paper, estimates for second and third MacLaurin coefficients of certain subclasses of bi-univalent functions in the open unit disk defined by convolution are determined, and certain special cases are also indicated.
Alkahtani, Badr +2 more
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