Symmetry vs. asymmetry.
-equivalences generated by shape function on the real line
This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.
Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers
In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically (C, 1, 1) summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively....
The A. M. -G. M. inequality as a rearrangement inequality.
The Affine Frame in -adic Analysis
In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of -adic number, hence provide new mathematic tools for application of -adic analysis.
The Banach–Mazur game and σ-porosity
It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.
The construction of some means.
The counterpart of Fan's inequality and its related results.
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
The generalized Heron mean and its dual form.
The inequalities in variables.
The intersection convolution of relations and the Hahn-Banach type theorems
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...
The laminary model of the exploded Descartes-plane.
The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...
The nonabsolute boundedness model of the theory of semisets
The optimal convex combination bounds for Seiffert's mean.
The optimal convex combination bounds of arithmetic and harmonic means for the Seiffert's mean.
The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means.
The optimization for the inequalities of power means.
The space of real-analytic functions has no basis
Let Ω be an open connected subset of . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.