[PDF] Top 20 Differential Subordination and Superordination of Analytic Functions Defined by an Integral Operator

... and let A(1) = A. Let f and F be members of H (U ). The function f (z) is said to be subordinate to F (z), or F(z) is said to be superordinate to f (z), if there exists a function ω(z) analytic in U with ω(0) = 0 ... See full document

... Carlson-Shaffer operator (see ...between analytic functions Miller et all [8] obtained some interesting subordination theorems involving certain ...considered subordination-preserving ... See full document

... differential superordination. An analytic func- tion q(z) is called a subordinant of the solutions of the strong differential superordination, or more simply a subordinant, if q(z) ≺ p(z) for all p(z) ... See full document

... of analytic functions in the open unit disk U which is defined by generalized Ruscheweyh di ff erential ...the integral means inequalities for the fractional derivatives of order p η 0 ≤ p ≤ n, ... See full document

... differential subordination between analytic func- tions and a linear operator defined for a certain family of analytic functions which are in- troduced here by means of these linear ... See full document

... some subordination theorems involving certain integral op- erators for analytic functions in U ...considered superordination- preserving properties of the integral ... See full document

... Lemma 2.2 Wilken and Feng 15, see also 16. Let μ be a positive measure on 0, 1 and let g be a complex-valued function defined on U × 0, 1 such that g·, t is analytic in U for each t ∈ 0, 1, and g z, · is ... See full document

... differential subordination, various subordination preserving properties for certain integral operators were obtained by Bulboac˘a 24, Miller et ...corresponding superordination properties and ... See full document

... order differential superordinations as well as superordination-preserving integral operators ...normalized analytic functions to ... See full document

... the differential subordination result of Miller and Mocanu [14, The- orem ...for functions associated with the operator I m p (λ, ℓ), and we obtain certain other related ...corresponding ... See full document

... of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, ...An analytic function is said to be univalent in a domain if it does not take the same ... See full document

... An analytic function q is called a subordinant of ...all functions p satisfying ...the functions h, q and φ for which the following implication ... See full document

... Darus, Differential Subordination Defined by New Generalised Derivative Operator for Analytic Functions, International Journal of Mathematics and Mathematical Sciences, Article ID 369078[r] ... See full document

... Strong differential subordination and superordination properties are determined for some families analytic functions in the open unit disk which are associated with the Komatu ... See full document

... Definition 1.1 (Oros and Gh Oros, [9]) Let 𝑓(𝑧, 𝜁), 𝑔(𝑧, 𝜁) analytic in 𝑈 × 𝑈̅. The function 𝑓(𝑧, 𝜁) is said to be strongly subordinate to 𝑔(𝑧, 𝜁), written 𝑓(𝑧, 𝜁) ≺≺ 𝐹(𝑧, 𝜁), 𝑧 ∈ 𝑈, 𝜁 ∈ 𝑈̅, if there exists an ... See full document

... are analytic in the open unit disc U {z ∈ C : |z| < 1} on the complex plane ...of functions that are univalent, starlike of order α, and convex of order α in U, ...convex functions in U, ...f ... See full document

... Abstract: In this paper, we introduce the class S α,λ n,s (β ), consisting of analytic functions defined by a generalized operator. We derive coefficient inequalities, growth and distortion ... See full document

... two functions f and g is denoted by f ≺ g and defined as f(z) = g(w(z)), where w(z) is schwarz function in f ...univalent functions, starlike functions and convex functions ...of ... See full document

... for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler type differential equation of order ... See full document

... the differential subordination theorem, we further investigate the subclass H λ n,γ [α, β ] of functions which are analytic in the unit ...Several subordination results on a con- vex ... See full document