Some Relationships Involving Subordination

Some Relationships Involving Subordination

If X(t) is a stochastic process taking values in some space 9C and g is a real-valued function on 9C then we may consider the process g(X(t)). Often from some knowledge about the process X(t) and the function g one can deduce properties of the process g(X(t)). For example: if X(t) is Brownian motion in R" and g is a subharmonic function on Rn that doesn't grow too fast then g(X(t)) is a semimar...

Subordination and Super Ordination Results Involving Certain Convolution Operators

Some applications of differential subordination

A number of interesting criteria were given by earlier workers for a normalized analytic function to be in the familiar class ∗ of starlike functions. The main object of the present paper is to extend and improve each of these earlier results. An application associated with an integral operator c(c >−1) is also considered.

Some Subordination Criteria concerning the Sǎlǎgean Operator

Applying Sǎlǎgean operator, for the class A of analytic functions f(z) in the open unit disk U which are normalized by f(0) = f ′(0) − 1 = 0, the generalization of an analytic function to discuss the starlikeness is considered. Furthermore, from the subordination criteria for Janowski functions generalized by some complex parameters, some interesting subordination criteria for f(z) ∈ A are given.

Certain Subordination Results Involving a Generalized Multiplier Transformation Operator

This paper investigates various new subordination results for certain p -valent analytic functions involving a generalized multiplier transformation operator Jm p (λ , l),m ∈ Z, defined recently by J. K. Prajapat [Math. Comput. Modelling, 55 (2012), 1456–1465]. Several lines of approach are followed to obtain the subordination results. We also consider some simpler and precise forms of the deri...