SUBORDINATION RESULTS FOR A FRACTIONAL INTEGRAL OPERATOR

In this paper, we establish several differential subordinations regarding the operator 𝐷^(−𝜆)_𝑧 𝑆𝑅^(𝑚,𝑛) defined using the fractional integral of the differential operator 𝑆𝑅^(𝑚,𝑛), obtained as a convolution product of Salagean operator 𝑆^𝑚 and Ruscheweyh derivative 𝑅^𝑛. By means of the newly obtain...

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Bibliographic Details
Published inIssues of analysis Vol. 11 (29); no. 1; pp. 20 - 31
Main Author A. Alb Lupaş
Format Journal Article
LanguageEnglish
Published Petrozavodsk State University 2022
Subjects
analytic function
convolution product
differential subordination
fractional integral
ruscheweyh derivative
salagean operator
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Summary:In this paper, we establish several differential subordinations regarding the operator 𝐷^(−𝜆)_𝑧 𝑆𝑅^(𝑚,𝑛) defined using the fractional integral of the differential operator 𝑆𝑅^(𝑚,𝑛), obtained as a convolution product of Salagean operator 𝑆^𝑚 and Ruscheweyh derivative 𝑅^𝑛. By means of the newly obtained operator, a new subclass of analytic functions denoted by 𝒮𝓡_(m,n,𝜆)(𝛿) is introduced and various properties and characteristics of this class are derived, makinguse of the concept of differential subordination.
ISSN:2306-3424
2306-3432
DOI:10.15393/j3.art.2022.10550