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 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 A Class of Integral Operators Preserving Subordination and Superordination for Analytic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
H. A. Al-Kharsani ◽  
N. M. Al-Areefi ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Type Theorem ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Sandwich Type

The purpose of the paper is to investigate several subordination- and superordination-preserving properties of a class of integral operators, which are defined on the space of analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function.

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 Sandwich-type theorems for certain integral operators

2010 ◽  
Vol 41 (3) ◽  
pp. 207-216
Author(s):  
H. A. Al-Kharsani ◽  
N. M. Al-Areefi
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Type Theorem ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sandwich Type

The purpose of the present paper is to obtain the sandwich-type theorem which contains the subordination-and superordination-preserving properties for certain integral operators defined on the space of normalized analytic functions in the open unit disk.

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 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 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 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.

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