scholarly journals New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2000
Author(s):  
Alina Alb Lupaş ◽  
Georgia Irina Oros
Keyword(s):  
Complex Analysis ◽  
Function Theory ◽  
Differential Subordination ◽  
Open Unit ◽  
Fuzzy Sets Theory ◽  
Geometric Function ◽  
New Applications ◽  
Sets Theory ◽  
Differential Subordinations ◽  
Theoretical Results

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lαm, given by Lαm:An→An, Lαmf(z)=(1−α)Rmf(z)+αSmf(z), where An={f∈H(U),f(z)=z+an+1zn+1+…,z∈U} is the subclass of normalized holomorphic functions and the operators Rmf(z) and Smf(z) are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator Lαm, a certain fuzzy class of analytic functions denoted by SLFmδ,α is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries.

scholarly journals Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2539
Author(s):  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Complex Analysis ◽  
Function Theory ◽  
Confluent Hypergeometric Function ◽  
Differential Subordination ◽  
Geometric Function Theory ◽  
Geometric Function ◽  
Hypergeometric Integral ◽  
Differential Subordinations

This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results.

scholarly journals On Lie ideals and $ (\sigma, \tau)$-Jordan derivations An application of Briot-Bouquet differential subordination

2002 ◽  
Vol 33 (1) ◽  
pp. 1-12
Author(s):  
Jagannath Patel
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Function Theory ◽  
Differential Subordination ◽  
Open Unit ◽  
Geometric Function Theory ◽  
Open Unit Disc ◽  
Geometric Function

By using the method of Briot-Bouquet differential subordination, we prove and sharpen some classical results in geometric function theory. We also derive some criteria for univalency for certain classes analytic functions in the open unit disc.

scholarly journals Subordination for multivalent analytic functions associated with Wright generalized hypergeometric function.

2013 ◽  
Vol 44 (1) ◽  
pp. 61-71
Author(s):  
J. Sokol ◽  
N. Sarkar ◽  
P. Goswami ◽  
J. Dziok
Keyword(s):  
Hypergeometric Function ◽  
Analytic Functions ◽  
Function Theory ◽  
Geometric Function Theory ◽  
Generalized Hypergeometric Function ◽  
Geometric Function ◽  
Differential Subordinations

Recently M. K. Aouf and T. M. Seoudy, (2011, {\it Integral Trans. Spec. Func.} {\bf 22}(6) (2011), 423--430) have introduced families of analytic functions associated with the Dziok--Srivastava operator. In this work we use the Dziok--Raina operator to consider classes of multivalent analytic functions. It is connected with Wright generalized hypergeometric function, see J. Dziok and R. K. Raina (2004, {\it Demonstratio Math.}, {\bf 37}(3) 533--542). Moreover, we present a new result which extends some of the earlier results and give other properties of these classes. We have made use of differential subordinations and properties of convolution in geometric function theory.

scholarly journals On The Third-Order Complex Differential Inequalities of ξ-Generalized-Hurwitz–Lerch Zeta Functions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 845
Author(s):  
Hiba Al-Janaby ◽  
Firas Ghanim ◽  
Maslina Darus
Keyword(s):  
Differential Inequality ◽  
Function Theory ◽  
Zeta Functions ◽  
Differential Subordination ◽  
Geometric Function Theory ◽  
Third Order ◽  
The Third ◽  
Geometric Function ◽  
Z Domain ◽  
Admissible Functions

In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order differential subordination for a newly defined linear operator that includes ξ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating the appropriate classes of admissible functions.

scholarly journals New Symmetric Differential and Integral Operators Defined in the Complex Domain

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 906 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Function Theory ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Function ◽  
Ruscheweyh Derivative ◽  
Symmetry Properties ◽  
Statistical Studies ◽  
Ordinary Derivative

The symmetric differential operator is a generalization operating of the well-known ordinary derivative. These operators have advantages in boundary value problems, statistical studies and spectral theory. In this effort, we introduce a new symmetric differential operator (SDO) and its integral in the open unit disk. This operator is a generalization of the Sàlàgean differential operator. Our study is based on geometric function theory and its applications in the open unit disk. We formulate new classes of analytic functions using SDO depending on the symmetry properties. Moreover, we define a linear combination operator containing SDO and the Ruscheweyh derivative. We illustrate some inclusion properties and other inequalities involving SDO and its integral.

scholarly journals Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
K. AL-Shaqsi
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Polylogarithm Function ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Strong Differential Subordination ◽  
Differential Subordinations ◽  
Admissible Functions

By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.

scholarly journals Teichmuller space theory and classical problems of geometric function theory

2021 ◽  
Vol 18 (2) ◽  
pp. 160-178
Author(s):  
Samue Krushkal
Keyword(s):  
Riemann Surfaces ◽  
Function Theory ◽  
Geometric Function Theory ◽  
Space Theory ◽  
New Approach ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Geometric Function ◽  
Coefficient Problems ◽  
New Applications

Recently the author has presented a new approach to solving the coefficient problems for holomorphic functions based on the deep features of Teichmüller spaces. It involves the Bers isomorphism theorem for Teichmüller spaces of punctured Riemann surfaces. The aim of the present paper is to provide new applications of this approach and extend the indicated results to more general classes of functions.

Some properties associated to a certain class of starlike functions

2019 ◽  
Vol 69 (6) ◽  
pp. 1329-1340 ◽  
Author(s):  
Vali Soltani Masih ◽  
Ali Ebadian ◽  
Sibel Yalçin
Keyword(s):  
Function Theory ◽  
Starlike Functions ◽  
Sharp Inequality ◽  
Open Unit ◽  
Geometric Function Theory ◽  
Open Unit Disk ◽  
Geometric Function ◽  
The Family ◽  
Logarithmic Coefficients ◽  
Dilogarithm Function

Abstract Let 𝓐 denote the family of analytic functions f with f(0) = f′(0) – 1 = 0, in the open unit disk Δ. We consider a class $$\begin{array}{} \displaystyle \mathcal{S}^{\ast}_{cs}(\alpha):=\left\{f\in\mathcal{A} : \left(\frac{zf'(z)}{f(z)}-1\right)\prec \frac{z}{1+\left(\alpha-1\right) z-\alpha z^2}, \,\, z\in \Delta\right\}, \end{array}$$ where 0 ≤ α ≤ 1/2, and ≺ is the subordination relation. The methods and techniques of geometric function theory are used to get characteristics of the functions in this class. Further, the sharp inequality for the logarithmic coefficients γn of f ∈ $\begin{array}{} \mathcal{S}^{\ast}_{cs} \end{array}$(α): $$\begin{array}{} \displaystyle \sum_{n=1}^{\infty}\left|\gamma_n\right|^2 \leq \frac{1}{4\left(1+\alpha\right)^2}\left(\frac{\pi^2}{6}-2 \mathrm{Li}_2\left(-\alpha\right)+ \mathrm{Li}_2\left(\alpha^2\right)\right), \end{array}$$ where Li2 denotes the dilogarithm function are investigated.

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