[PDF] Top 20 Some applications of differential subordinations in the geometric function theory

... the geometric function ...differential subordinations. The main result in the theory of differential subordinations was introduced by Miller and Mocanu in [, ...A function p, ... See full document

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

... Lemma  ([]) Let μ be a positive measure on the unit interval [, ]. Let g (z, t) be a complex valued function defined on U × [, ] such that g(, t) is analytic in U for each t ∈ [, ] and such that g(z, ) ... See full document

... Analytic Function Theory, World Scientific Publishing ...Waniurski, Some classes of functions subordinate to linear trans- formation and their applications, ... See full document

... Cătaş, On certain classes of p-valent functions defined by multiplier transformations, in Proceedings of the International Symposium on Geometric Function Theory and Applications, İst[r] ... See full document

... This operator contains many known operators as its special cases for different values of μ and b; see [] for a complete list of such operators. This paper by Srivastava and Attiya discusses some interesting ... See full document

... The purpose of the present paper is to investigate interesting new results in connec- tion with differential subordination and to improve some results obtained by Miller and Mocanu []. Also we remark that the ... See full document

... point theory is one of the most rapidly growing topic of nonlinear functional anal- ...analysis, differential and integral equations, functional analysis, oper- ator theory, topology and algebraic ... See full document

... the Theory of Inequalities due to the fact that other inequalities such as the generalised triangle inequality, the arithmetic mean-geometric mean inequality, H¨ older and Minkowski inequalities, Ky Fan’s ... See full document

... the Theory of Inequalities due to the fact that other inequalities such as the arithmetic mean- geometric mean inequality, H¨ older and Minkowski inequalities, Ky Fan’s inequality ... See full document

... To use theorems and corollaries listed in the previous section we put instead of the function p some functionals over the class An, such as pz fz/z, pz zf z/fz or the others. In this way the inclusion ... See full document

... Section 7 addresses questions of geometric G-conjugacy versus rational G-conjugacy. In particular, here we prove Theorem 1.5(i), (ii) (first assertion) and (iv) (see Corollary 7.2). We close the section with a ... See full document

... A number of extensions of the Banach contraction principle have appeared in literature. One of its most important extensions is known as Caristi’s fixed point theorem. It is well known that Caristi’s fixed point theorem ... See full document

... Shakhmurov, VB: Embedding theorems and maximal regular differential operator equations in Banach-valued function spaces.. Triebel, H: Interpolation Theory, Function Spaces, Differential [r] ... See full document

... for some c  0 , is called a Lyapunov surface or a level surface. A geometric integrator for a system of ordinary differential equations with a Lyapunov function V should preserve V as a ... See full document

... Krylov and Bogoliubov’s first book, published initially in 1934, was translated to English by Solomon Lefschetz in 1942 (Krylov & Bogoliubov, 1950). As he em- phasized, the authors Krylov and Bogoliubov considered ... See full document

... tenets: differential association theory and learning ...transmission theory also supports the contentions of the two aforementioned ...theories. Differential association theory, coined ... See full document

... If f and g are analytic functions in U, we say that f is subordinate to g, written f ≺ g, if there is a function w analytic in U, with w() = , |w(z)| < , for all z ∈ U such that f (z) = g(w(z)) for all z ∈ ... See full document

... We obtain several results concerning the 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

... Basic equations of stream field over helicopter rotor are formulated, their decomposition is made and mean induced velocity harmonics are integrally presented. Theoretical basis of hypergeometric function ... See full document