We study the spectral zeta functions of the Laplacian on self-similar fractals. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of self-similar sets such that their complex dimensions are not on the imaginary axis, which allows us to interpret...

For analytic functions f(z) and g(z) which satisfy the subordination f(z) ≺ g(z), J. E. Littlewood (Proc. London Math. Soc., 23 (1925), 481–519) has shown some interesting results for integral means of f(z) and g(z). The object of the present paper is to derive some applications of integral means by J.E. Littlewood and show interesting examples for our theorems. We also generalize the results o...

We obtain subordination and superordination preserving properties for the Saigo type generalized fractional differ-integral operator, defined for multivalent functions in the open unit disk. A differential sandwich-type theorem for these multivalent function, and some consequences are also presented.

Let Ap(n) be the class of analytic and multivalent functions f(z) in the open unit disk U. Furthermore, let Sp(n, α) and Tp(n, α) be the subclasses of Ap(n) consisting of multivalent starlike functions f(z) of order α and multivalent convex functions f(z) of order α, respectively. Using the coefficient inequalities for f(z) to be in Sp(n, α) and Tp(n, α), new subclasses S∗ p (n, α) and T ∗ p (n...