We prove sharp bounds on eigenvalues of the Laplacian that complement the Faber–Krahn and Luttinger inequalities. In particular, we prove that the ball maximizes the first eigenvalue and minimizes the spectral zeta function and heat trace. The normalization on the domain incorporates volume and a computable geometric factor that measures the deviation of the domain from roundness, in terms of m...

We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes.

We create two Sakaguchi-type function classes that are starlike and convex with respect to their symmetric points, including a q-difference operator, which may have or assymetric properties, in the open unit disc. first obtain sufficient coefficient bounds for these functions. In view of bounds, we quasi-Hadamard products several partial sums classes. Moreover, special values parameters provide...

An analytic functions f(z) defined on 4 = {z : |z| < 1} and normalized by f(0) = 0, f ′(0) = 1 is starlike with respect to conjugate points

The object of the present paper is to prove a criterion for p-valently starlike functions in the open unit disk.

We investigate the conditions under which the solution of the initial-boundary value problem of the non-local equation ut = u + λ f (u)/( ∫ Ω f (u) dx) p , where Ω is a bounded domain of RN and f (u) is a positive, increasing, convex function, performs blow-up. c © 2005 Elsevier Ltd. All rights reserved.