is finite. The purpose of this paper is to provide a framework for proving inequalities of the form (1). The idea is to exploit the close relationship of the Fourier transform to the operation of convolution and then to apply techniques from the theory of positive integral operators. Although the convolution operators that arise are not necessarily positive, they are trivially majorized by posi...

We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, Sα, for α ∈ (0, 1). We establish necessary and sufficient conditions for equality in the continuity bound and prove that these conditions are the same for every member of the family. Our result builds on recent work in which we constructed a st...

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms f : Ω onto −→ Ω∗ between bounded doubly connected domains such that ModΩ 6 ModΩ∗ there exists, unique up to conformal authomorphisms of Ω, an energy-minimal diffeomorphism. No boundary conditions are imposed on f . Although any energyminimal diffeomorphis...

the purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. the results in this paper improve and extend the corresponding results of xu and ori, zhou and chang, sun, yang and yu in some aspects.

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

Let n be a positive integer. We may write (or split) n as sums of n nonincreasing nonnegative integers p1, p2, . . . , pn in different ways (or partitions; see Section 2). For example, 3 = 3 + 0 + 0 = 2 + 1 + 0 = 1 + 1 + 1. If we denote by P (n) the number of different partitions of n, then P (3) = 3. One may check that P (5) = 7. As n gets large, P (n) increases rapidly. It is astounding that ...

A vector x E Rn is weakly k-majorized by a vector q 6 R^ if the sum of r largest components of x is less than or equal to the sum of r largest components of q for r = 1,2,. . . , k and k < n. In this paper we extend the components of x to their absolute values in the above description and generalize some results in [2] and [3] by G. Dahl and F. Margot.

We describe the convex set of the eigenvalues of hermitian matrices which are majorized by sum of m hermitian matrices with prescribed eigenvalues. We extend our characterization to selfadjoint nonnegative (definite) compact operators on a separable Hilbert space. We give necessary and sufficient conditions on the eigenvalue sequence of a selfadjoint nonnegative compact operator of trace class ...

In this paper, we introduce the concept of free abstract fuzzy economy and, using Wu’s existence theorem of maximal elements for lower semicontinuous correspondences [26] and Kim and Lee’s existence theorems of best proximity pairs [14], we prove the existence of fuzzy equilibrium pairs for free abstract fuzzy economies first with upper semicontinuous and then with lower semicontinuous constrai...