Inequality for power series with nonnegative coefficients and applications

We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well

Bounding the Čebyšev function for a differentiable function whose derivative is h or λ-convex in absolute value and applications

Some bounds for the Čebyšev functional of a differentiable function whose derivative is h or λ-convex in absolute value and applications for functions of selfadjoint operators in Hilbert spaces via the spectral representation theorem are given

Trace inequalities of Shisha-Mond type for operators in Hilbert spaces

Some trace inequalities of Shisha-Mond type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given