[PDF] Top 20 Sandwich Theorems for Some Analytic Functions Defined by Convolution

... g(z) ≺ ϕ € h(z), zh ′ (z), z 2 h ′′ (z); z Š , (2) a function q ∈ H(U) is called a subordinant of (2), if q(z) ≺ h(z) for all the functions h satisfying (2). A univalent subordinant e q that satisfies q(z) ≺ e ... See full document

... Recently several authors, Shanmugam et al. [13], Goyal et al. [4], Murugusundaramoorthy and Magesh [11, 12], Magesh et al. [9], Ibrahim and Darus [6], Wanas [16,17], Wanas and Joudah [18], Wanas and Majeed [20] and Wanas ... See full document

... are analytic functions in U , we say that f is subordinate to g, written f ≺ g if there exists a Schwarz function w, which (by definition) is analytic in U with w(0) = 0 and |w(z)| < 1 for all z ∈ ... See full document

... univalent functions, Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in ...p-valent functions defined by integral operators, ... See full document

... [7] R. M. Ali, V. Ravichandran, M. Hussain Khan and K. G. Subramanian, “Differential Sandwich Theorems for Cer- tain Analytic Functions,” Far East Journal of Mathe- matical Sciences, Vol. 15, ... See full document

... An analytic function q (z) is called a subordinant of the solutions of the differential superordination (4) if q (z) ≺ p (z) for all p (z) satisfying ...normalized analytic functions to ... See full document

... are analytic and univalent in the open unit disk U = {z : z ∈ C , |z| < 1} ...are analytic functions in U , we say that f is subordinate to g, written f ≺ g if there exists a Schwarz function w, ... See full document

... of analytic functions defined by convolution with a fixed analytic function are ...introduced. Convolution properties of these classes which include the classical classes of ... See full document

... It is obvious that I λ s (I λ t f (z)) = I λ s+t f (z) for all real numbers s and t. The operator I λ s has been studied by several authors for di ff erent choices of s and λ, see [4–7]. It is worth noting that, for s any ... See full document

... Let A denote the class of analytic function satisfying the condition f(0) = f ’ (0) - 1 = 0 in the open unit disc U = {z : | z |< 1} . By S, C, S*, C*, and K we means the well-known subclasses of A which ... See full document

... A continuous function f = u + iv is a complex-valued harmonic function in a simply con- nected complex domain D ⊂ C if both u and v are real harmonic in D. It was shown by Clunie and Sheil-Small [] that such a harmonic ... See full document

... By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disc are introduced and some unifying re[r] ... See full document

... Ponnusamy, “Univalence and starlikeness of certain transforms defined by convolution of analytic functions,” Journal of Mathematical Analysis and Applications, vol.. Bao, “Some propertie[r] ... See full document

... = (λ+p) D λ+p f (z)−λ D λ+p−1 f (z) (λ > −p; p ∈ N ; z ∈ U ) (4.4) in (1.3), then Theorem 2 corresponds to the known result of Dinggong and Liu [3, p. 129, Theorem 4]. The operator D λ+p−1 used in (4.4) is the ... See full document

... multivalent functions which are defined by means of ...derived. Some (known or new) special cases of the multivalent function classes, which are investigated here, are also ... See full document

... The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk. Relevant connec- tions of the results, ... See full document

... [6] defined by Saitoh and Ruschweyh derivative operator [23] (for detail one may refer to [8, ...the convolution (4) reduces to the Salagean operator [24] ... 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

... A function f ∈ A is said to be bi-univalent in D if both f (z) and f −1 (z) are univalent in D. We denote by Σ the class of all functions f(z) which are bi-univalent functions in D . We say that f is ... See full document

... then fz is said to be strongly convex of order β and type α in U, and denoted by Cα, β. It is obvious that fz ∈ A belongs to Cα, β if and if zf z ∈ S ∗ α, β. Further, we note that S ∗ α, 1 ≡ S ∗ α and Cα, 1 ≡ Cα which ... See full document