An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of Bernstein–Kantorovich operators involving shape parameters λ,α and a positive integer as an original extension of Bernstein–Kantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.

Summability is a particularly fertile field for functional analysis application. Summability through functional analysis has become one of the most fascinating disciplines since it contains both interesting and challenging issues. In this paper, we aim to introduce four new sectional properties for topological sequence spaces: sectional weakly absolute convergence (WAC), sectional weak boundedness (WB), sectional weakly p -absolute convergence W p AC , and sectional weakly bounded variation (WBV). We have, also, investigate some of their relations and identities.

This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters α and λ and a positive integer. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem is given by a weighted A-statistical convergence. A Korovkin-type theorem is provided for the univariate and bivariate cases of the blending-type operators. Moreover, the convergence behavior of the univariate and bivariate new blending basis and new blending operators are exhaustively demonstrated by computer graphics. The studied univariate and bivariate blending-type operators reduce to the well-known Bernstein operators in the literature for the special cases of shape parameters α and λ, and they propose better approximation results.

For a non-decreasing sequence of the positive integers tending to infinity λ = (λ m ) such that λ m+1 − λ m ≤ 1, λ 1 = 1; (V, λ )-summability defined as the limit of the generalized de la Valée-Pousin of a sequence, [10]. In the present research, we establish some Tauberian, Abelian and Core theorems related to the (V, λ )-summability.

Music genre classification has a significant role in information retrieval for the organization of growing collections of music. It is challenging to classify music with reliable accuracy. Many methods have utilized handcrafted features to identify unique patterns but are still unable to determine the original music characteristics. Comparatively, music classification using deep learning models has been shown to be dynamic and effective. Among the many neural networks, the combination of a convolutional neural network (CNN) and variants of a recurrent neural network (RNN) has not been significantly considered. Additionally, addressing the flaws in the particular neural network classification model, this paper proposes a hybrid architecture of CNN and variants of RNN such as long short-term memory (LSTM), Bi-LSTM, gated recurrent unit (GRU), and Bi-GRU. We also compared the performance based on Mel-spectrogram and Mel-frequency cepstral coefficient (MFCC) features. Empirically, the proposed hybrid architecture of CNN and Bi-GRU using Mel-spectrogram achieved the best accuracy at 89.30%, whereas the hybridization of CNN and LSTM using MFCC achieved the best accuracy at 76.40%.