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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| Vydané v: | Advances in difference equations Ročník 2021; číslo 1; s. 1 - 11 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
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Cham
Springer International Publishing
21.07.2021
Springer Nature B.V SpringerOpen |
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| ISSN: | 1687-1847, 1687-1839, 1687-1847 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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
$\frac{1}{2}$
1
2
and convexity of order
$\frac{1}{2}$
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. 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. Abstract 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 $\frac{1}{2}$ and convexity of order 1 2 $\frac{1}{2}$ 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. 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 12 and convexity of order 12 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. |
| ArticleNumber | 342 |
| Author | Oros, Georgia Irina |
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| References | Alexander (CR1) 1915; 17 de Branges (CR4) 1985; 154 Libera (CR6) 1965; 16 Miller, Mocanu (CR11) 2000 Srivastava (CR16) 2020; 44 Dziok, Srivastava (CR5) 1999; 103 CR8 Oros (CR14) 2021; 13 Miller, Mocanu (CR9) 1978; 65 Strohhäcker (CR17) 1933; 37 Lupaş, Oros (CR7) 2021; 13 Oros (CR13) 2021; 13 Bernardi (CR3) 1969; 135 Antonino, Miller (CR2) 2020; 10 Miller, Mocanu (CR10) 1981; 28 Srivastava (CR15) 2007; 1 Mocanu, Bulboacă, Sălăgean (CR12) 1999 J. Dziok (3497_CR5) 1999; 103 S.S. Miller (3497_CR9) 1978; 65 P.T. Mocanu (3497_CR12) 1999 E. Strohhäcker (3497_CR17) 1933; 37 S.S. Miller (3497_CR11) 2000 S.D. Bernardi (3497_CR3) 1969; 135 R.J. Libera (3497_CR6) 1965; 16 S.S. Miller (3497_CR10) 1981; 28 G.I. Oros (3497_CR14) 2021; 13 H.M. Srivastava (3497_CR15) 2007; 1 A.A. Lupaş (3497_CR7) 2021; 13 H.M. Srivastava (3497_CR16) 2020; 44 J.W. Alexander (3497_CR1) 1915; 17 J.A. Antonino (3497_CR2) 2020; 10 G.I. Oros (3497_CR13) 2021; 13 L. de Branges (3497_CR4) 1985; 154 3497_CR8 |
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| Snippet | Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric... Abstract Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer)... |
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| SubjectTerms | 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 |
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| Title | Study on new integral operators defined using confluent hypergeometric function |
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