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 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 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 Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 259
Author(s):  
Georgia Irina Oros
Keyword(s):  
Hypergeometric Function ◽  
Complex Plane ◽  
Complex Analysis ◽  
Type Theorem ◽  
Confluent Hypergeometric Function ◽  
Differential Subordination ◽  
Real Plane ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Dual Notion

The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.

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 New Applications of the Fractional Integral on Analytic Functions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 423
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Hypergeometric Function ◽  
Analytic Functions ◽  
Fractional Integral ◽  
Type Theorem ◽  
Confluent Hypergeometric Function ◽  
Sandwich Type ◽  
Original Part ◽  
New Applications ◽  
Differential Subordinations ◽  
Published Paper

The fractional integral is a function known for the elegant results obtained when introducing new operators; it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories.

scholarly journals Differential Subordination and Superordination for Srivastava-Attiya Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Type Theorem ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

Due to the well-known Srivastava-Attiya operator, we investigate here some results relating thep-valent of the operator with differential subordination and subordination. Further, we obtain some interesting results on sandwich-type theorem for the same.

Differential sandwich theorems of p-valent functions defined by a certain linear operator

2016 ◽  
Vol 53 (2) ◽  
pp. 131-137
Author(s):  
Ping He ◽  
Defei Zhang
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

In this paper we introduce differential subordination and superordination properties for certain subclasses of analytic functions involving certain linear operator, and obtain sandwich-type results for the functions belonging to these classes.

scholarly journals Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2041
Author(s):  
Georgia Irina Oros
Keyword(s):  
Analytic Functions ◽  
Dual Problem ◽  
Differential Subordination ◽  
Research Subject ◽  
Harmonic Complex ◽  
Differential Superordination ◽  
Complex Valued ◽  
Differential Subordinations

The theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination for the harmonic complex-valued functions and have defined the differential superordination for harmonic complex-valued functions. Finding the best subordinant of a differential superordination is among the main purposes in this research subject. In this article, conditions for a harmonic complex-valued function p to be the best subordinant of a differential superordination for harmonic complex-valued functions are given. Examples are also provided to show how the theoretical findings can be used and also to prove the connection with the results obtained in 2015.

Sandwich results for analytic functions involving with iterations of the Owa–Srivastava operator and its combination

2014 ◽  
Vol 07 (04) ◽  
pp. 1450063
Author(s):  
Madan Mohan Soren
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Strong Differential Subordination

In this paper, we investigate some strong differential subordination and strong differential superordination results for analytic functions, which involving the iterations of the Owa–Srivastava operator and its combination. Some new sandwich type results are also obtained.

"Some Results of Differential Subordination and Superordination for Univalent Functions

2021 ◽  
Vol 8 (1) ◽  
pp. 91-97
Author(s):  
Ihsan A. Abbas
Keyword(s):  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Type Result ◽  
Best Dominant ◽  
Subordination Chain ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

"Let 1 and 2 belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions to satisfy the double subordination chain 1() ≺() ≺ 2() , then we obtain 1() is the best subordinant, 2() is the best dominant. Also we derive some sandwich –type result.

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