A Theil coefficient-based combination prediction method with interval heterogeneous information for wind energy prediction

This paper constructs the continuous-Young optimal weighted arithmetic averaging (C-YOWA) operator and the continuous-Young optimal weighted geometric (C-YOWG) operator based on definite integral and Young inequality. A series of special cases and main properties of the proposed aggregation operators are also investigated. In order to integrate heterogeneous interval data and obtain more accurate prediction results, the heterogeneous interval combination prediction (HICP) model based on C-YOWA operator, C-YOWG operator and Theil coefficient is proposed. The HICP model consider not only the existence of both additive and multiplicative interval information, but also the preference information of experts. Finally, the model is applied to the empirical analysis of wind energy prediction. The comparison of results shows that the established model can effectively improve the accuracy of prediction.

Further generalized refinement of Young’s inequalities for τ -mesurable operators

In this paper, we prove that if a, b > 0 and 0 ≤ v ≤ 1. Then for all positive integer m(1) - For v ∈ v \in \left[ {0,{1 \over {{2^n}}}} \right], we have {\left( {{a^v}{b^{1 - v}}} \right)^m} + \sum\limits_{k = 1}^n {{2^{k - 1}}{v^m}{{\left( {\sqrt {{b^m}} - \root {{2^k}} \of {\left( {a{b^{2k - 1}} - 1} \right)m} } \right)}^2} \le {{\left( {va + \left( {1 - v} \right)b} \right)}^m}.}(2) - For v ∈ v \in \left[ {{{{2^n} - 1} \over {{2^n}}},1} \right], we have {\left( {{a^v}{b^{1 - v}}} \right)^m} + \sum\limits_{k = 1}^n {{2^{k - 1}}{{\left( {1 - v} \right)}^m}{{\left( {\sqrt {{a^m}} - \root {{2^k}} \of {\left( {b{a^{2k - 1}} - 1} \right)m} } \right)}^2} \le {{\left( {va + \left( {1 - v} \right)b} \right)}^m},} we also prove two similar inequalities for the cases v ∈ v \in \left[ {{{{2^n} - 1} \over {{2^n}}},{1 \over 2}} \right] and v ∈ v \in \left[ {{1 \over 2},{{{2^n} + 1} \over {{2^n}}}} \right]. These inequalities provides a generalization of an important refinements of the Young inequality obtained in 2017 by S. Furuichi. As applications we shall give some refined Young type inequalities for the traces, determinants, and p-norms of positive τ-measurable operators.

Refined Young Inequality and Its Application to Divergences

We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weighted arithmetic mean and the weighted geometric mean. Applying the newly obtained inequalities, we show some results on the Tsallis divergence, the Rényi divergence, the Jeffreys–Tsallis divergence and the Jensen–Shannon–Tsallis divergence.

On the Multilinear Fractional Transforms

In this paper we first introduce multilinear fractional wavelet transform on Rn×R+n using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff–Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces.

PDα-type iterative learning control with initial state learning for fractional-order systems

In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PDα-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PDα-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

Some Refinements of the Numerical Radius Inequalities via Young Inequality

In this paper, we get an improvement of the Hölder-McCarthy operator inequality in the case when r ≥ 1 and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.

Fenchel Duality Theory and a Primal-Dual Algorithm on Riemannian Manifolds

This paper introduces a new notion of a Fenchel conjugate, which generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its properties, e.g., the Fenchel–Young inequality and the characterization of the convex subdifferential using the analogue of the Fenchel–Moreau Theorem. These properties of the Fenchel conjugate are employed to derive a Riemannian primal-dual optimization algorithm and to prove its convergence for the case of Hadamard manifolds under appropriate assumptions. Numerical results illustrate the performance of the algorithm, which competes with the recently derived Douglas–Rachford algorithm on manifolds of nonpositive curvature. Furthermore, we show numerically that our novel algorithm may even converge on manifolds of positive curvature.

Improved Young and Heinz operator inequalities with Kantorovich constant

UDC 517.9 We present numerous refinements of the Young inequality by the Kantorovich constant. We use these improved inequalities to establish corresponding operator inequalities on a Hilbert space and some new inequalities involving the Hilbert – Schmidt norm of matrices.

Further generalization, refinements of the Young inequality

In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.

A new generalization of two refined Young inequalities and applications

In this paper, we prove that if a, b > 0 and 0 ≤ α ≤ 1, then for m = 1, 2, 3, . . . ,\matrix{ {r_0^m{{\left( {{a^{{m \over 2}}} - {b^{{m \over 2}}}} \right)}^2}} & { \le r_0^m\left( {{{{b^{m + 1}} - {a^{m + 1}}} \over {b - a}} - \left( {m + 1} \right){{\left( {ab} \right)}^{{m \over 2}}}} \right)} \cr {} & { \le {{\left( {\alpha a + \left( {1 - \alpha } \right)b} \right)}^m} - {{\left( {{a^\alpha }{b^{1 - \alpha }}} \right)}^m},} \cr }where r0 = min{α, 1 – α }. This is a considerable new generalization of two refinements of the Young inequality due to Kittaneh and Manasrah, and Hirzallah and Kittaneh, which correspond to the cases m = 1 and m = 2, respectively. As applications we give some refined Young type inequalities for generalized euclidean operator radius and the numerical radius of some well-know f -connection of operators and refined some Young type inequalities for the traces, determinants, and norms of positive definite matrices.