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- Title
Second-Order Differential Superordination for Analytic Functions With Fixed Initial Coefficient.
- Authors
Mendiratta, Rajni; Nagpal, Sumit; Ravichandran, V.
- Abstract
Appropriate modifications are made to the theory of second order differential superordination developed by Miller and Mocanu to investigate the analytic functions in the unit disk D with fixed initial coefficient; in particular, a suitable class Φβ of functions is determined for which the following implication is satisfied: 𝛗∈ Φβ and Ω ⊂ {'𝛗(p(z), zp′(z), z2p′′(z); z) : z ∈ D} ⇒ Δ ⊂ p(D), where Ω and Δ are sets in ℂ, 𝛗(r, s, t; z) : ℂ3×D → ℂ and p is analytic in D with fixed initial coefficient β. Several interesting examples are also provided.
- Subjects
ANALYTIC functions; COEFFICIENTS (Statistics); SET theory; LATTICE theory; UNIVALENT functions
- Publication
Southeast Asian Bulletin of Mathematics, 2015, Vol 39, Issue 6, p851
- ISSN
0129-2021
- Publication type
Article