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Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators
- Source :
- Mathematics, Volume 9, Issue 19, Mathematics, Vol 9, Iss 2487, p 2487 (2021)
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
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 Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+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 Lαm are established and the best subordinant is given for each strong differential superordination.
- Subjects :
- convex function
Subordination (linguistics)
extended Sălăgean differential operator
Pure mathematics
General Mathematics
Holomorphic function
Derivative
strong differential superordination
extended Ruscheweyh derivative
Operator (computer programming)
best subordinant
QA1-939
Computer Science (miscellaneous)
Convex function
Engineering (miscellaneous)
Mathematics
Differential (mathematics)
Analytic function
Subjects
Details
- ISSN :
- 22277390
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....8385b12e6d4ffdbee1a3fa3d0358f057