Let be the class of functions which are analytic in open unit disk and having form . Denote to for all that univalent Then, let denote bi-univalent In this paper, we obtain second Hankel determinant certain classes function defined by subordinations particular, determine initial coefficients obtained upper bound functional

Let f and F be members of H. The function f is said to be subordinate to F, or F is said to be superordinate to f , if there exists a functionw analytic in U, withw 0 0 and |w z | < 1, and such that f z F w z . In such a case, we write f ≺ F or f z ≺ F z . If the function F is univalent in U, then we have f ≺ F if and only if f 0 F 0 and f U ⊂ F U cf. 1 . Definition 1.1 see 1 . Let φ : C2 → C a...

Syntactic trees, or phrase markers, have originally been suggested as a representation of syntax in the mind based on purely linguistic grounds. In this paper, the psychological reality of syntactic trees and hierarchical ordering is explored from another perspective--that of the neuropsychology of language breakdown. The study reported here examined several syntactic domains that rely on diffe...

Recently the present authors established refined versions of Bohr's inequality in case bounded analytic functions. In this article, we state and prove a generalization these results. Here, consider image origin boundary unit disk under function question let distance between both play central role our theorems. Thereby extend Bohr for class quasi-subordinations which contains classes majorizatio...

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

Here, we study strong differential subordinations for the extended new operator IR?,lm defined by Hadamard product of multiplier transformation Im,?,l and Ruscheweyh derivative Rm, on class normalized analytic functions An??={f?H(U×U¯),f(z,?)=z+an+1?zn+1+?,z?U,??U¯}, IR?,lm:An???An??, IR?,lmfz,?=Im,?,l?Rmfz,?.

The main objective of this paper is to present classical second-order differential subordination knowledge extended in study include new results regarding third-order subordinations. focus on the problems examined by theory. Hence, obtained here reveal techniques for identifying dominants and best dominant certain Another aspect novelty application Gaussian hypergeometric function. Novel are us...