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Let Ɓ be a unital Banach algebra, let a ∈ Ɓ, G be a convex domain of ℂ with σ(a) ⊂ G, let α, β ∈ G, and let f : G → ℂ be analytic on G. By using the analytic functional calculus, we obtain (among others) the following result: ‖ f (a) - 1 2 ∑ k = 0 n 1 k ! [ f (k) (α) (a - α) k + (- 1) k f (k) (β) (β - a) k ] ‖ ≤ 1 2 (n + 1) ! [ ‖ a - α ‖ n + 1 + ‖ β - a ‖ n + 1 ] × m a x { sup s ∈ [ 0 , 1 ] ‖ f (n + 1) [ (1 - s) α + s a ] ‖ , sup s ∈ [ 0 , 1 ] ‖ f (n + 1) [ (1 - s) α + s β ] ‖ }. Some examples of exponential functions on Banach algebras are also presented. [ABSTRACT FROM AUTHOR]

On utilizing the spectral representation of self-adjoint operators in Hilbert spaces, some error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert Spaces via a Taylor's type expansion are given. [ABSTRACT FROM AUTHOR]

Some Jensen's type inequalities for Log-Convex functions of self-adjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided. [ABSTRACT FROM AUTHOR]

In this survey we present some recent results obtained by the author in extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators defined on complex Hilbert spaces. [ABSTRACT FROM AUTHOR]

Some reverses of the Jensen inequality for functions of self-adjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided. [ABSTRACT FROM AUTHOR]

We establish some new Fejér-type inequalities for convex functions. [ABSTRACT FROM AUTHOR]

The article presents research on the attainment of a sharp bound of the čebyšev functional for the Riemann-Stieltjes integral and applications in investigations. The applications for quadrature rules such as trapezoid and midpoint rules were given. The general perturbed quadrature rule and error estimates were obtained in this study. The inequality of the notation were also presented in the investigation. The bounded variation and the Riemann integrals were also attained in its observation. jdhfjauiioqtijtri

The article presents a study which examines the inequalities of the Güss type for the numerical radius of bounded linear operators in Hilbert spaces. It recalls some classical results involving the numerical radius of two linear operators A,B. The general results for the product of the linear operators are given The proof of these results are also provided. In addition, the findings of some particular cases of interest are also given and proof of some of the study's included.

General divergence measures for probability distributions are introduced and their main properties established. Connections with f-divergence corresponding to a convex function fare explored. [ABSTRACT FROM AUTHOR]

Some new sufficient conditions for the weighted Čebyšev's inequality for real numbers to hold are provided [ABSTRACT FROM AUTHOR]

Some error estimates in terms of thep—norms of the fourth derivative for the remainder in a perturbed trapezoid formula are given. Applications for the expectation of a random variable and the Hermite-Hadamard divergence in Information Theory are also pointed out. [ABSTRACT FROM AUTHOR]

A variety of bounds are obtained for the variance and expectation of a continuous random variable whose p.d.f. is defined over a finite interval. Previous results are shown to be particular cases of the current more general development. [ABSTRACT FROM AUTHOR]

An Ostrowski type integral inequality for the Riemann-Stieltjes integral ∫abƒ (t) du (t), where ƒ is assumed to be of bounded variation on [a,b] andu is ofr-H- Hölder type on the same interval, is given. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out. [ABSTRACT FROM AUTHOR]

Some trapezoid and mid-point type inequalities related to the Hermite–Hadamard inequality on the disk of center C = (a , b) and radius R, D (C , R) ⊆ R 2 , are investigated. It is shown that the estimated value obtained in the trapezoid and mid-point type inequalities has a relation with the integral of the partial derivative of the considered function on ∂ (C , R) , the boundary of D (C , R) . [ABSTRACT FROM AUTHOR]

This paper deals with some new theorems and inequalities about a Fejér type integral inequality which estimate the difference between the right and middle part in Fejér inequality with new bounds. Also some applications to higher moments of random variables, an error estimate for trapezoidal formula, and some inequalities in connection with special means are given. [ABSTRACT FROM AUTHOR]