CLASSES OF FIRST-ORDER DIFFERENTIAL SUPERORDINATIONS

By T. Bulboacă. 2002

230 citations recorded by the source corpus.

Let ip : C 2 —> C be an analytic function in a domain A C C 2 , let p an analytic function in the unit disc U such that ip(p(z), zp'(z)) is univalent in U and suppose that p satisfies the first-order differential superordination h(z) tp(p(z),zp'(z)). In the case when <p(p(z), zp (z)) = a(p(z)) + P(p(z)) j(zp'(z)) we determine conditions on h, a, 0 and 7 so that the above subordination implies q(z) -< p(z), where q is the largest function so that q(z) -< p(z) for all p functions satisfying the first-order differential superordination. The concept of differential superordination was introduced by S. S. Miller and P. T. Mocanu in [2] like a dual problem of differential subordination [1],

Subfields: Applied Mathematics, Mechanical Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2f62048e268748770d4861c6bb1bb772aa384cd1

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In Applied Mathematics

In Mechanical Engineering

In Numerical Analysis

Citations in the corpus

Classes of Multivalent Functions Defined by Dziok-Srivastava Linear Operator and Multiplier Transformation (2006, result): “Using the results of Miller and Mocanu [13], Bulboacă have considered certain classes of first order differential superordinations [3] and superordination-preserving integral operators [2].”
CLASSES OF MEROMORPHIC α-CONVEX FUNCTIONS (2010, unknown): “If f ∈ Σ, −zf ′(z)/f(z) ∈ H[1, 1] ∩Q and zf ′(z) f(z) + α z2f ′′(z) f(z) is univalent in ∆ and (α− 1)q(z) + αq(2)(z) − αzq′(z) ≺ zf ′(z) f(z) + α z(2)f ′′(z) f(z) ,”
Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations (2006, methodology): “[2] Bulboacă, T., 2002, Classes of first-order differential superordinations.”