AN EXTENSION OPERATOR ASSOCIATED WITH CERTAIN $G$-LOEWNER CHAINS

Properties of multivalent functions associated with certain integral operator

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

An Operator Extension of Bohr's inequality

Certain subclasses of bi-univalent functions associated with the Aghalary-Ebadian-Wang operator

In this paper, we introduce and investigate two new subclasses of the functions class $ Sigma $ of bi-univalent functions defined in the open unit disk, which are associated with the Aghalary-Ebadian-Wang operator. We  estimate the coefficients $|a_{2} |$ and  $|a_{3} |$ for functions in these new subclasses. Several  consequences of the result are also pointed out.

Loewner Matrices and Operator Convexity

Let f be a function from R+ into itself. A classic theorem of K. Löwner says that f is operator monotone if and only if all matrices of the form [ f(pi)−f(pj) pi−pj ] are positive semidefinite. We show that f is operator convex if and only if all such matrices are conditionally negative definite and that f(t) = tg(t) for some operator convex function g if and only if these matrices are conditio...

properties of multivalent functions associated with certain integral operator

let a(p) denote the class of functions which are analytic in the open unit disk u. by making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.