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Inequalities Of Lipschitz Type For Power Series In Banach Algebras

Sever S. Dragomir — 2015

Annales Mathematicae Silesianae

Let [...] f(z)=∑n=0∞αnzn $f (z) = \sum_{n = 0}^{\infty} α_{n} z^{n}$ be a function defined by power series with complex coefficients and convergent on the open disk D (0, R) ⊂ ℂ, R > 0. For any x, y ∈ ℬ, a Banach algebra, with ‖x‖, ‖y‖ < R we show among others that [...] ‖f(y)−f(x)‖≤‖y−x‖∫01fa′(‖(1−t)x+ty‖)dt $∥f (y) - f (x)∥ \leq ∥y - x∥ \int_{0}^{1} f_{a}^{'} (∥(1 - t) x + t y∥) d t$ where [...] fa(z)=∑n=0∞|αn| zn $f_{a} (z) = \sum_{n = 0}^{\infty} | α_{n} | z^{n}$ . Inequalities for the commutator such as [...] ‖f(x)f(y)−f(y)f(x)‖≤2fa(M)fa′(M)‖y−x‖, $∥f (x) f (y) - f (y) f (x)∥ \leq 2 f_{a} (M) f_{a}^{'} (M) ∥y - x∥,$ if ‖x‖, ‖y‖ ≤ M < R, as well as some inequalities of Hermite–Hadamard type are also provided.

Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Sever S. Dragomir — 2016

Annales Mathematicae Silesianae

Some reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.

Some new inequalities of Hermite-Hadamard type for GA-convex functions

Sever S. Dragomir — 2018

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

Some new inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given. Refinements and weighted version of known inequalities are provided. Some applications for special means are also obtained.

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Currently displaying 1 – 20 of 25

Inequalities Of Lipschitz Type For Power Series In Banach Algebras

Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Some new inequalities of Hermite-Hadamard type for GA-convex functions

A survey of recent reverses for the generalised triangle inequality in inner product spaces

Bounds for some perturbed Čeby'ev functionals.

Reverses of the triangle inequality in Banach spaces.

An inequality of Ostrowski type via Pompeiu's mean value theorem.

Vector and operator trapezoidal type inequalities for continuous functions of selfadjoint operators in Hilbert spaces.

A survey of some recent inequalities for the norm and numerical radius of operators in Hilbert spaces.

Grüss type inequalities for forward difference of vectors in inner product spaces.

A potpourri of Schwarz related inequalities in inner product spaces. II.

Norm inequalities for sequences of operators related to the Schwarz inequality.

The hypo-Euclidean norm of an $n$ -tuple of vectors in inner product spaces and applications.

Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation.

A potpourri of Schwarz related inequalities in inner product spaces. I.

On some inequalities in normed algebras.

A theorem of Rolewicz's type for measurable evolution families in Banach spaces.

Iterative refinements of the Hermite-Hadamard inequality, applications to the standard means.

On the stability of generalized d'Alembert and Jensen functional equations.

On the weighted Ostrowski inequality.