Here we are dealing with smooth functions from a real box to a Banach space. For these we establi... more Here we are dealing with smooth functions from a real box to a Banach space. For these we establish vector multivariate sharp Ostrowski type inequalities to all possible directions.
Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fracti... more Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.
Here are used the left general fractional derivatives Caputo style with respect to a base absolut... more Here are used the left general fractional derivatives Caputo style with respect to a base absolutely continuous strictly increasing function g. We mention various examples of such fractional derivatives for di¤erent g. Let f be r-times continuously di¤erentiable function on [a; b], and let L be a linear left general fractional di¤erential operator such that L(f) is non-negative over a critical closed subinterval I of [a; b]. We can find a sequence of polynomials Q_n of degree less-equal n such that L(Q_n) is non-negative over I, furthermore f is fractionally and simultaneously approximated uniformly by Q_n over [a; b]. The degree of this constrained approximation is given by inequalities using the high order modulus of smoothness of f(r). We nish with applications of the main fractional monotone approximation theorem for different g.
We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequali... more We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequalities over $\mathbb{R}$ of fractional orders $2 < \alpha \leq 3 $. These estimate the size of first and second derivatives of a composition with a Banach space valued function over $\mathbb{R}$. We give applications when $α = 2.5$.
We give uniform and Lp Caputo-Bochner abstract sequential generalized right fractional Landau ine... more We give uniform and Lp Caputo-Bochner abstract sequential generalized right fractional Landau inequalities over $\mathbb{R}_{-}$. These estimates the size of second and third sequential abstract generalized right fractional derivatives of a Banach space valued function over $\mathbb{R}_{-}$. We give an application when the basic fractional order is 1
Here we present Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte types fractional ... more Here we present Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and ψ-Hilfer fractional derivatives. All estimates are with respect to norms ·p, 1≤p≤∞. At the end we provide applications.
Here we study the approximation of functions by a great variety of Max-Product operators under di... more Here we study the approximation of functions by a great variety of Max-Product operators under differentiability. These are positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. We improve known related results which do not use smoothness of functions..
Here we are dealing with smooth functions from a real box to a Banach space. For these we establi... more Here we are dealing with smooth functions from a real box to a Banach space. For these we establish vector multivariate sharp Ostrowski type inequalities to all possible directions.
Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fracti... more Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.
Here are used the left general fractional derivatives Caputo style with respect to a base absolut... more Here are used the left general fractional derivatives Caputo style with respect to a base absolutely continuous strictly increasing function g. We mention various examples of such fractional derivatives for di¤erent g. Let f be r-times continuously di¤erentiable function on [a; b], and let L be a linear left general fractional di¤erential operator such that L(f) is non-negative over a critical closed subinterval I of [a; b]. We can find a sequence of polynomials Q_n of degree less-equal n such that L(Q_n) is non-negative over I, furthermore f is fractionally and simultaneously approximated uniformly by Q_n over [a; b]. The degree of this constrained approximation is given by inequalities using the high order modulus of smoothness of f(r). We nish with applications of the main fractional monotone approximation theorem for different g.
We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequali... more We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequalities over $\mathbb{R}$ of fractional orders $2 < \alpha \leq 3 $. These estimate the size of first and second derivatives of a composition with a Banach space valued function over $\mathbb{R}$. We give applications when $α = 2.5$.
We give uniform and Lp Caputo-Bochner abstract sequential generalized right fractional Landau ine... more We give uniform and Lp Caputo-Bochner abstract sequential generalized right fractional Landau inequalities over $\mathbb{R}_{-}$. These estimates the size of second and third sequential abstract generalized right fractional derivatives of a Banach space valued function over $\mathbb{R}_{-}$. We give an application when the basic fractional order is 1
Here we present Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte types fractional ... more Here we present Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and ψ-Hilfer fractional derivatives. All estimates are with respect to norms ·p, 1≤p≤∞. At the end we provide applications.
Here we study the approximation of functions by a great variety of Max-Product operators under di... more Here we study the approximation of functions by a great variety of Max-Product operators under differentiability. These are positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. We improve known related results which do not use smoothness of functions..
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Papers by GEORGE ANASTASSIOU