scholarly journals Third-order differential subordination and superordination involving a fractional operator

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Muhammad Zaini Ahmad ◽  
Hiba F. Al-Janaby
Keyword(s):  
Fractional Integral ◽  
Differential Subordination ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Fractional Differential ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

AbstractThe third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

scholarly journals Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huo Tang ◽  
H. M. Srivastava ◽  
Shu-Hai Li ◽  
Li-Na Ma
Keyword(s):  
Unit Disk ◽  
Differential Subordination ◽  
Convolution Operators ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Order Case ◽  
Differential Superordination ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

There are many articles in the literature dealing with the first-order and the second-order differential subordination and superordination problems for analytic functions in the unit disk, but only a few articles are dealing with the above problems in the third-order case (see, e.g., Antonino and Miller (2011) and Ponnusamy et al. (1992)). The concept of the third-order differential subordination in the unit disk was introduced by Antonino and Miller in (2011). Let Ω be a set in the complex planeC. Also letpbe analytic in the unit diskU=z:z∈C  and  z<1and suppose thatψ:C4×U→C. In this paper, we investigate the problem of determining properties of functionsp(z)that satisfy the following third-order differential superordination:Ω⊂ψpz,zp′z,z2p′′z,z3p′′′z;z:z∈U. As applications, we derive some third-order differential subordination and superordination results for meromorphically multivalent functions, which are defined by a family of convolution operators involving the Liu-Srivastava operator. The results are obtained by considering suitable classes of admissible functions.

scholarly journals Applications of third order differential subordination and superordination involving generalized struve function

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3047-3059 ◽  
Author(s):  
Priyabrat Gochhayat ◽  
Anuja Prajapati
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Third Order ◽  
The Third ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Struve Functions ◽  
Differential Subordinations ◽  
Admissible Functions

In the present paper, by making use of the linear operator associated with generalized Struve functions suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type results are established for a class of univalent analytic functions involving generalized Struve functions. Relevant connections of the new results presented here with those that were considered in earlier works are pointed out.

scholarly journals An integrodifferential operator for meromorphic functions associated with the Hurwitz-Lerch zeta function

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 2045-2057 ◽  
Author(s):  
Adel Attiya ◽  
Sang Kwon ◽  
Park Hyang ◽  
Nak Cho
Keyword(s):  
Zeta Function ◽  
Meromorphic Functions ◽  
Differential Subordination ◽  
Open Disk ◽  
Third Order ◽  
The Third ◽  
Integrodifferential Operator ◽  
Lerch Zeta Function ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

In this paper, we introduce a new integrodifferential operator associated with the Hurwitz Lerch Zeta function in the puncture open disk of the meromorphic functions. We also obtain some properties of the third-order differential subordination and superordination for this integrodifferential operator, by using certain classes of admissible functions.

scholarly journals Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2601
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Fractional Integral ◽  
Type Theorem ◽  
Confluent Hypergeometric Function ◽  
Differential Subordination ◽  
Best Dominant ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Differential Subordination And Superordination ◽  
New Applications ◽  
Differential Subordinations

The fractional integral of confluent hypergeometric function is used in this paper for obtaining new applications using concepts from the theory of fuzzy differential subordination and superordination. The aim of the paper is to present new fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. The original theorems proved in the paper generate interesting corollaries for particular choices of functions acting as fuzzy best dominant and fuzzy best subordinant. Another contribution contained in this paper is the nice sandwich-type theorem combining the results given in two theorems proved here using the two theories of fuzzy differential subordination and fuzzy differential superordination.

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.

scholarly journals Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 327
Author(s):  
Alina Alb Lupaş ◽  
Georgia Irina Oros
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Type Theorem ◽  
Confluent Hypergeometric Function ◽  
Differential Subordination ◽  
Different Types ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Differential Subordination And Superordination ◽  
Complex Valued

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.

scholarly journals Applications of differential subordinations involving a generalized fractional differintegral operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hanaa M. Zayed ◽  
Teodor Bulboacă
Keyword(s):  
Differential Subordination ◽  
Third Order ◽  
The Third ◽  
Fractional Differintegral ◽  
Differential Subordinations ◽  
Fractional Differintegral Operator ◽  
Admissible Functions

Abstract Using the third-order differential subordination basic results, we introduce certain classes of admissible functions and investigate some applications of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator.

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 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 Admissible classes of multivalent functions associated with an integral operator

2019 ◽  
Vol 73 (1) ◽  
pp. 57
Author(s):  
Tamer Seoudy ◽  
Mohamed Aouf
Keyword(s):  
Integral Operator ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

In this paper we investigate some applications of the differential subordination and superordination of classes of admissible functions associated with an integral operator. Additionally, differential sandwich-type results are obtained.

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