scholarly journals Fuzzy Differential Subordination of the Atangana–Baleanu Fractional Integral

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1929
Author(s):  
Alina Alb Lupaş ◽  
Adriana Cătaş
Keyword(s):  
Fractional Integral ◽  
Bessel Functions ◽  
Differential Subordination ◽  
Analytical Functions ◽  
Differential Subordinations

The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana–Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.

scholarly journals An Application of the Principle of Differential Subordination to Analytic Functions Involving Atangana–Baleanu Fractional Integral of Bessel Functions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 971
Author(s):  
Alina Alb Lupaş ◽  
Adriana Cătaş
Keyword(s):  
Analytic Functions ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Differential Subordination

The aim of this paper is to establish certain subordination results for analytic functions involving Atangana–Baleanu fractional integral of Bessel functions. Studying subordination properties by using various types of operators is a technique that is widely used.

scholarly journals On Special Differential Subordinations Using Fractional Integral of Sălăgean and Ruscheweyh Operators

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1553
Author(s):  
Alina Alb Lupaş ◽  
Georgia Irina Oros
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Fractional Integral ◽  
Differential Subordination ◽  
Differential Subordinations

In the present paper, a new operator denoted by Dz−λLαn is defined by using the fractional integral of Sălăgean and Ruscheweyh operators. By means of the newly obtained operator, the subclass Snδ,α,λ of analytic functions in the unit disc is introduced, and various properties and characteristics of this class are derived by applying techniques specific to the differential subordination concept. By studying the operator Dz−λLαn, some interesting differential subordinations are also given.

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 On Certain Differential Subordination of Harmonic Mean Related to a Linear Function

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 966
Author(s):  
Anna Dobosz ◽  
Piotr Jastrzębski ◽  
Adam Lecko
Keyword(s):  
Convex Function ◽  
Linear Function ◽  
Differential Subordination ◽  
Harmonic Mean ◽  
Best Dominant ◽  
Symmetry Properties ◽  
Differential Subordinations ◽  
Difficult Issue

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

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 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.

scholarly journals Criteria for Strongly Starlike Functions

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Neng Xu
Keyword(s):  
Unit Disk ◽  
Starlike Functions ◽  
Differential Subordination ◽  
Strongly Starlike Functions ◽  
Strongly Starlike ◽  
Differential Subordinations

Let f(z) be analytic in the unit disk U={z:|z|<1} with f(0)=f'(0)-1=0 and (f(z)/z)f'(z)≠0. By using the method of differential subordinations, we determine the largest number α(β,λ,μ,m) such that, for some β,λ,μ, and m, the differential subordination λzf'(z)/f(z)1-μ1+(zf''(z)/f'(z))-zf'(z)/f(z)+zf'(z)/f(z)m≺1+z/1-zα(β,λ,μ,m)(z∈U) implies zf'(z)/f(z)≺1+z/1-zβ. Some useful consequences of this result are also given.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

scholarly journals Applications of Differential Subordination for Argument Estimates of Multivalent Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Meng-Ting Lu ◽  
Ting Jia ◽  
Xing-Qian Ling ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Differential Subordinations

By using the method of differential subordinations, we derive some properties of multivalent analytic functions. All results presented here are sharp.

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