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The Berezin symbol à A of an operator A on the reproducing kernel Hilbert space H(Ω) over some set with the reproducing kernel k is defined by ... In this paper, we obtain some new inequalities for Berezin symbols of operators on reproducing kernel Hilbert spaces by using classical Hermite-Hadamard inequality and convex functions. Some other related questions are also discussed. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to show that Cheney-Sharma Chlodovsky operators preserve properties of the function of modulus of continuity and Lipschitz condition of a given Lipschitz continuous function f: Furthermore, we give a result for these operators when f is a convex function. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to derive some results for multivalent analytic functions defined by a linear operators. As a special case of these results, we obtain several sufficient conditions for close-to-convexity and starlikeness of certain analytic functions. [ABSTRACT FROM AUTHOR]

In this paper we prove the Hadamard and the Fejér-Hadamard inequalities for convex functions via Caputo fractional derivatives. We also derive some related inequalities for n-time differentiable functions f(n) such that |f(n)|q; q ≥ 1 is convex, by using Caputo fractional derivatives. [ABSTRACT FROM AUTHOR]

In this paper we present some new operator inequality for convex functions. We have obtained a number of Jensen's type inequalities for convex and operator convex functions of self-adjoint operators for positive linear maps. Some results are exemplified for power and logarithmic functions. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the coefficient estimates for functions in certain new subclasses of starlike and convex functions of complex order γ, which are introduced by means of a generalized differential operator and non-homogeneous Cauchy-Euler type differential equation. Several corollaries and consequences of the main results are also obtained. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new subclass Mp(n, α, c) of analytic and multivalent functions in the unit disk which includes the class Sp(n, α) of multivalent starlike functions of order α and the class Tp(n, α) of multivalent convex functions of order α . Using generalized Bernardi Libera integral operator and H ölder's inequality, some interesting properties of convolution for the class Mp(n, α, c) are considered [ABSTRACT FROM AUTHOR]

In the present article, our aim is to investigate the problem of obtaining upper bounds for |T2(2)|, |T2(3)|, |T3(2)| and |T3(1)|, which are special cases of the symmetric Toeplitz determinant for functions belonging to the M(λ; n) subclass. [ABSTRACT FROM AUTHOR]

In this work, the authors introduced new subfamilies of ω-starlike and ω-convex functions with negative coefficient with respect to other points. The coefficient estimates for these classes are obtained. Also relevant connection to classical Fekete-Zsego theorem is briefly discussed. [ABSTRACT FROM AUTHOR]

Let Φ1,…, Φn be strictly positive linear maps from a unital C*-algebra A into a C*-algebra B and let Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. Φi be unital. If f is an operator convex function on an interval J, then for every self-adjoint operator A ∈ A with spectrum contained in J, the following refinement of the Choi-Davis-Jensen inequality holds: Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. [ABSTRACT FROM AUTHOR]