We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasinormal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. ...

We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2+ε moments outside the sphere of radius O( √ k). In the specific case...

In this paper, we introduce a new class of operators on Hilbert space called (f*-Ҩ) quasi binormal operator order ղ. We study and give some its properties.

The papers [21], [8], [23], [25], [24], [5], [7], [6], [19], [4], [1], [2], [18], [10], [22], [13], [3], [20], [16], [15], [9], [12], [11], [14], and [17] provide the terminology and notation for this paper. Let X be a non empty set and let f , g be elements of X . Then g · f is an element of X . One can prove the following propositions: (1) Let X, Y , Z be real linear spaces, f be a linear ope...

In this paper some new positive results in the Operator Corona Problem are obtained in rather general situation. The main result is that under some additional assumptions about a bounded analytic operator-valued function F in the unit disc D the condition F (z)F (z) ≥ δI ∀z ∈ D (δ > 0) implies that F has a bounded analytic left inverse. Typical additional assumptions are (any of the following):...

The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since more than tw...

where u and 4~ denote scalar functions on R 2, and g is a scalar function on R. We shall assume g and ff continuous, and we shall determine sufficient conditions in the form of inequalities to guarantee that problem (1) has continuous solutions. Thus, the solutions which we consider will be weak solutions in the sense of distributions. In terms of functional analysis and the alternative approac...

We give some characterizations of self-adjointness and symmetricity of operator monotone functions by using the Barbour transform f → t+f 1+f and show that there are many non-symmetric operator means between the harmonic mean ! and the arithmetic mean ∇. Indeed, we show that there exists a non-symmetric operator mean between any two symmetric operator means.

The Dynamical Systems Method (DSM) is justified for solving operator equations F (u) = f , where F is a nonlinear operator in a Hilbert space H. It is assumed that F is a global homeomorphism of H onto H, that F ∈ C loc, that is, it has a continuous with respect to u Fréchet derivative F ′(u), that the operator [F ′(u)]−1 exists for all u ∈ H and is bounded, ||[F ′(u)]−1|| ≤ m(u), where m(u) > ...