Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

Alina Alb Lupaş and Georgia Irina Oros
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Alina Alb Lupaş: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania

Mathematics, 2021, vol. 9, issue 19, 1-12

Abstract: The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U × U ¯ having as coefficients holomorphic functions in U ¯ . Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as L α m : A n ζ * → A n ζ * , L α m f ( z , ζ ) = ( 1 − α ) R m f ( z , ζ ) + α S m f ( z , ζ ) , z ∈ U , ζ ∈ U ¯ , where R m f ( z , ζ ) is the extended Ruscheweyh derivative, S m f ( z , ζ ) is the extended Sălăgean operator and A n ζ * = { f ∈ H ( U × U ¯ ) , f ( z , ζ ) = z + a n + 1 ζ z n + 1 + ⋯ , z ∈ U , ζ ∈ U ¯ } . This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U × U ¯ . Several strong differential superordinations concerning the operator L α m are established and the best subordinant is given for each strong differential superordination.

Keywords: strong differential superordination; convex function; best subordinant; extended Sălăgean differential operator; extended Ruscheweyh derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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