Kudriasov Type Univalence Criteria for Some Integral Operators

Pescar, Virgil; Breaz, Nicoleta

doi:10.1155/2013/721932

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…, this integral operator is a generalization of the integral operator introduced by Pescar and Owa in [23] . v) For α i − 1 = 0, k i (z) = z and k i (z) = 1 we obtain the integral operator which was defined and studied by Pescar [22]…”

Section: Introductionmentioning

confidence: 95%

Some univalence conditions related to a general integral operator

Bărbatu

Breaz

2020

General Mathematics

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For some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢n, that was introduced in a recent work [1] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu’s and the Pescar’s univalence criteria, as well as the Mocanu’s and Şerb’s Lemma. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.

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Section: Introductionmentioning

confidence: 95%

Some univalence conditions related to a general integral operator

Bărbatu

Breaz

2020

General Mathematics

View full text Add to dashboard Cite

show abstract

“…this integral operator is a generalization of the integral operator introduced by Pescar and Owa in [22] . v) For α i − 1 ≡ α i and γ i = 0 we obtain the integral operator which was defined and studied by Pescar in [20]…”

Section: Introductionmentioning

confidence: 99%

Univalence criteria for a general integral operator

Bărbatu

Breaz

2020

Filomat

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For some classes of analytic functions f and 1 in the open unit disk U, we consider the general integral operatorMn, that was introduced in a recent work [2] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu?s and the Pescar?s univalence criteria. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.

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On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions

et al. 2022

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In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our discussions were the Kudriasov conditions for the univalency of functions, as well as functional inequalities for the generalized Bessel functions. We included the conditions for the univalency of integral operators that involve Bessel, modified Bessel and spherical Bessel functions as special cases. Furthermore, we provided sufficient conditions for the integral operators that involve trigonometric, as well as hyperbolic, functions as an application of our results.

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Kudriasov Type Univalence Criteria for Some Integral Operators

Abstract: We consider some integral operators defined by analytic functions in the open unit disk and derive new univalence criteria for these operators, using Kudriasov condition for a function to be univalent.

Cited by 3 publications

References 6 publications

Some univalence conditions related to a general integral operator

Some univalence conditions related to a general integral operator

Univalence criteria for a general integral operator

On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions

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