Using the results of third-order differential subordination, we introduce certain families admissible functions and discuss some applications subordination for meromorphic associated with a linear operator containing generalized Mittag-Leffler function.

We obtain a representation of the derivative of the spectral shift function ξ(λ, h) in the framework of semi-classical ”black box” perturbations. Our representation implies a meromorphic continuation of ξ(λ, h) involving the semi-classical resonances. Moreover, we obtain a Weyl type asymptotics of the spectral shift function as well as a Breit-Wigner approximation in an interval (λ− δ, λ+ δ), 0...

Abstract This paper studies analytic functions f defined on the open unit disk of complex plane for which / g and (1 + z ) are both with positive real part some function . We determine radius constants these to belong classes strong starlike functions, order ? , parabolic as well associated lemniscate Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential a particular rationa...

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.

To shift the path of integration to the left, one needs at least meromorphic continuation to some half-plane R s > r− δ as well as some information on the growth and the distribution of the poles of Φr. Assuming the Riemann hypothesis, Egami and Matsumoto[4] described the behavior for the case r = 2. In addition to the RH, parts of their results depend on unproved assumptions on the distributio...