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 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 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 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 Differential Subordination Results for Certain Integrodifferential Operator and Its Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
M. A. Kutbi ◽  
A. A. Attiya
Keyword(s):  
Number Theory ◽  
Zeta Function ◽  
Function Theory ◽  
Analytic Number Theory ◽  
Differential Subordination ◽  
Geometric Function Theory ◽  
Integrodifferential Operator ◽  
Analytic Number ◽  
Geometric Function ◽  
Lerch Zeta Function

We introduce an integrodifferential operatorJs,b(f) which plays an important role in theGeometric Function Theory. Some theorems in differential subordination forJs,b(f) are used. Applications inAnalytic Number Theoryare also obtained which give new results for Hurwitz-Lerch Zeta function and Polylogarithmic function.

scholarly journals The problem of extreme decomposition of a complex plane with fixed poles on a circle

2018 ◽  
Vol 32 ◽  
pp. 10-17
Author(s):  
Liudmyla Vyhivska
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Complex Plane ◽  
Complex Analysis ◽  
Function Theory ◽  
Geometric Function Theory ◽  
Holomorphic Dynamics ◽  
Geometric Function ◽  
Inner Radius ◽  
Overlapping Domains

The problem of extreme decomposition of a complex plane with fixed poles on a circle. Investigation on geometric function theory has been conducted by several researchers, however, few studies have reported on the problem considering extremal configurations the product of inner radii of non-overlapping domains with respect to fixed poles. The paper describes the problem of finding the maximum of the product of inner radii of mutually non-overlapping symmetric domains with respect to points on a unit circle multiply by a certain positive degree \(\gamma\) of the inner radius of the domain with respect to the zero. The problem was studied using the method of separating transformation. Proving the theorem shows that the maximum is obtained if \(\gamma\in(1,n^2]\) and for all \(n\geqslant 2\). Its results and the method for the obtaining of these results can be used in the theory of potential, approximations, holomorphic dynamics, estimation of the distortion problems in conformal mapping, and complex analysis.

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 Fuzzy Differential Sandwich Theorems Involving the Fractional Integral of Confluent Hypergeometric Function

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1992
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Type Theorem ◽  
Confluent Hypergeometric Function ◽  
Differential Subordination ◽  
Best Dominant ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Differential Subordination And Superordination ◽  
Differential Subordinations

The operator defined as the fractional integral of confluent hypergeometric function was introduced and studied in previously written papers in view of the classical theory of differential subordination. In this paper, the same operator is studied using concepts from the theory of fuzzy differential subordination and superordination. The original theorems contain fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. Interesting corollaries are obtained for particular choices of the functions acting as fuzzy best dominant and fuzzy best subordinant. A nice sandwich-type theorem is stated combining the results given in two theorems proven in this paper using the two dual theories of fuzzy differential subordination and fuzzy differential superordination.

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