be the Fourier cosine series. The problem of L-convergence of the Fourier cosine series (1.1) has been settled for various special classes of coefficients. Young [9] found that an logn = o(1), n → ∞ is a necessary and sufficient condition for the L-convergence of the cosine series with convex (△an ≥ 0) coefficients, and Kolmogorov [8] extended this result to the cosine series with quasi-convex ( ∞

In this paper, we consider a problem in calculus of variations motivated by quantitative isoperimetric inequality the plane. More precisely, aim article is computation minimum variational $$\begin{aligned}\inf _{u\in {\mathcal {W}}} \frac{\displaystyle \int _{-\pi }^{\pi }[(u')^2-u^2]d\theta }{\displaystyle \left[ } |u| d\theta \right] ^2} \end{aligned}$$ where function $$u\in {W}}$$ $$H^1(-\pi...

Abstract In this article, by virtue of expansions two finite products finitely many square sums, with the aid series composite functions (hyperbolic) sine and cosine inverse functions, in light properties partial Bell polynomials, author establishes Taylor’s real powers containing squares terms Stirling numbers first kind, presents a closed-form formula specific polynomials at sequence derivati...

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

Dynamic economic dispatch (DED) deals with the allocation of predicted load demand over a certain period time among thermal generating units at minimum fuel cost. The objective function DED becomes highly complex and nonlinear after considering various operating constraints like valve point loading, ramp rate limit, transmission loss, generation limits. In this study, sine-cosine algorithm has ...

INTRODUCTION K-nearest neighbor (k-NN) classification is conventional non-parametric classifier, which has been used as the baseline classifier in many pattern classification problems. It is based on measuring the distances between the test data and each of the training data to decide the final classification output. CASE DESCRIPTION Since the Euclidean distance function is the most widely us...

In this article, a memristor chaotic system is constructed by introducing cosine function flux control memristor. By analyzing the balance of system, it found that there are coexisting attractors, and because periodicity function, has infinite attractors. The complexity analysis Spectral Entropy (SE) C0 used in paper to intuitively show complex dynamic characteristics system. addition, introduc...

Abstract This paper is devoted to studying the approximate controllability for second-order impulsive differential inclusions with infinite delay. For proving main results, we use results related cosine and sine function of operators, Martelli’s fixed point theorem, when combined properties inclusions. Firstly, prove initial conditions. Then, extend discussion system nonlocal Finally, provide a...

A classic result, in its early form due to Cox [2], states that if A is a normed algebra with a unity denoted by 1 and a is an element of A such that supn∈N ‖a− 1‖ < 1, then a = 1. Cox’s version concerned the case of square matrices of a given size. This was later extended to bounded operators on Hilbert space by Nakamura and Yoshida [6], and to an arbitrary normed algebra by Hirschfeld [4] and...