We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges. Kergin interpolation is a generalization of both Lagrange interpolation in the one dimensional case, and the Taylor polynomial in the case where all interpolation points coincide. In several vari...

A topological group G is extremely amenable if every continuous action of G on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe’s result, we sh...

We revisit a classical scenario in communication theory: a source is generating a waveform which we sample at regular intervals; we wish to transform the signal in such a way as to minimize distortion in its reconstruction, despite noise. The transformation must be online (also called causal), in order to enable real-time signaling. The noise model we consider is adversarial `1-bounded; this is...

A direct approach is used to establish both Ball and Barthe’s reverse isoperimetric inequalities for the unit balls of subspaces of Lp. This approach has the advantage that it completely settles all the open uniqueness questions for these inequalities. Affine isoperimetric inequalities generally have ellipsoids as extremals. The so called reverse affine isoperimetric inequalities usually have s...

in this paper, we prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. to prove the theorem, we use a non compatible condition, that is, weak commutativity of type (kb). we show that completeness of the whole space is not necessary for the existence and uni...

Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...