Study on new integral operators defined using confluent hypergeometric function

Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2021; no. 1; pp. 1 - 11
Main Author: Oros, Georgia Irina
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 21.07.2021
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Convex analysis
Convexity
Difference and Functional Equations
Difference Equations
Functional Analysis
Hypergeometric functions
Integrals
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Special Functions and Orthogonal Polynomials
30C45
30C80
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions, and that they extend starlikeness of order 1 2 and convexity of order 1 2 to starlikeness and convexity, respectively. For obtaining the original results, the method of admissible functions is used, and the results are also written as differential inequalities and interpreted using inclusion properties for certain subsets of the complex plane. The example provided shows an application of the original results.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03497-4