In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...

In this paper, we present weighted integral inequalities of Hermite-Hadamard type for differentiable preinvex and prequasiinvex functions. Our results, on the one hand, give a weighted generalization of recent results for preinvex functions and, on the other hand, extend several results connected with the Hermite-Hadamard type integral inequalities. Applications of the obtained results are prov...

A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast DHT algorithms and a multiplication-free fast algorithm for the Hadamard Transform. Key-words Discrete transforms, Hartley transform, Hadamard Transform.

Keywords: m-convex functions Hermite–Hadamard inequalities Hölder inequality Power-mean inequality a b s t r a c t In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m-convex.

An existence result for the solution set of a system of simultaneous generalized vector quasi-equilibrium problems (for short, (SSGVQEP)) is obtained, which improves Theorem 3.1 of the work of Ansari et al. (J. Optim. Theory Appl. 127:27-44, 2005). Moreover, a definition of Hadamard-type well-posedness for (SSGVQEP) is introduced and sufficient conditions for Hadamard well-posedness of (SSGVQEP...

We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order n is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.

This paper proposes a fast algorithm for Walsh Hadamard Transform on sliding windows which can be used to implement pattern matching most efficiently. The computational requirement of the proposed algorithm is about 1.5 additions per projection vector per sample which is the lowest among existing fast algorithms for Walsh Hadamard Transform on sliding windows.

Let A = (a j ) be an orthogonal matrix with no entries zero. Let B = (b j ) be the matrix defined by b j = 1 ai j . M. Kontsevich conjectured that the rank of B is never equal to three. We interpret this conjecture geometrically and prove it. The geometric statment can be understood as a generalization of the Castelnouvo lemma and Brianchon’s theorem in algebraic geometry. §1. Definitions and S...

Motivated by the success of classical random walks and chaotic dynamical systems, we study the quantisation of the random walk over Z and its relationships with a classical chaotic system x → 2xmod1, x ∈ [0,1]. In the physics literature, quantum random walks have been studied, for instance, by Ambainis et al. [1] and Konno et al. [8, 9]. In [8], Konno shows that the quantum random walk over Z c...