σ-asymptotically lacunary statistical equivalent sequences

This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S _σ,8-asymptotically equivalent of multiple L provided that for every ε > 0

An exact, closed-form solution for equilibrium of trveling, sagged, elastic cables under uniformly distributed loading

IntroctionThquilibrium of sagged, elastic cable s under its own weight loading is needed in tiledesign of cable structures. In 1851 RO'htsLll first investigated a uniform, inextensible suspendedchain hanging freely under its own weight. Ro.th[Zj considered a model of a heterogeneouschain hanging in the form of a cycloid, and application of this model to the uniform chainreduced to the Rohrs model when the sag ratio is small. However, the chain was modeled asinextensible. Pugsley['] develope…     

Almost periodic Szeg? cocycles with uniformly positive Lyapunov exponents

We exhibit examples of almost periodic Verblunsky coefficients for which Herman’s subharmonicity argument applies and yields the result that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point.     

The structure of uniformly Gâteaux smooth Banach spaces

It is shown that a Banach spaceX admits an equivalent uniformly Gateaux smooth norm if and only if the dual ball ofX* in its weak star topology is a uniform Eberlein compact. Supported by AV 101-97-02, AV 1019003 and GA ČR 201-98-1449. Supported by GA ČR 201-98-1449, AV 1019003 and GAUK 1/1998.     

Estimates of the Hölder constant for functions satisfying a uniformly elliptic or a uniformly parabolic quasilinear inequality with unbounded coefficients

One obtains inner and boundary estimates of the Hölder constants for functions u(·) satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality of nondivergence form with unbounded coefficients. It is shown that the Hölder exponents in them depend only on the dimension W and on the constants and occurring in the ellipticity conditions. In the boundary estimates they depend also on the constant ₀, occurring in the condition (A) on the boundary and on the Hölder exponent for the boundary values of u(·).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 72–94, 1985.     

A uniformly stable Fortin operator for the Taylor–Hood element

We construct a new Fortin operator for the lowest order Taylor–Hood element, which is uniformly stable both in $L^2$ and $H^1$ . The construction, which is restricted to two space dimensions, is based on a tight connection between a subspace of the Taylor–Hood velocity space and the lowest order Nedelec edge element. General shape regular triangulations are allowed for the $H^1$ -stability, while some mesh restrictions are imposed to obtain the $L^2$ -stability. As a consequence of this construction, a uniform inf–sup condition associated the corresponding discretizations of a parameter dependent Stokes problem is obtained, and we are able to verify uniform bounds for a family of preconditioners for such problems, without relying on any extra regularity ensured by convexity of the domain.     

Multi-valued totally quasi-ϕ-asymptotically nonexpansive semi-groups and strong convergence theorems in banach spaces

The purpose of this article is first to introduce the concept of multi-valued totally Quasi?-asymptotically nonexpansive semi-groups, which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi?-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.     

Convergence theorems of a modified hybrid algorithm for a family of quasi-φ-asymptotically nonexpansive mappings

The purpose of this article is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The results of this paper improve and extend the results of S. Matsushita and W. Takahashi (J. Approx. Theory, 134: 257–266 (2005)), T.H. Kim, H.K. Xu (Nonlinear Anal. 64: 1140–1152 (2006)), Y.F. Su, D.X. Wang, M.J. Shang (Fixed Point Theory Appl. 2008: 284613 (2008)) and others.     

Convergence theorems for mixed equilibrium problems, variational inequality problem and uniformly quasi-?-asymptotically nonexpansive mappings

We introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-?-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problems. Then, we obtain strong convergence theorems for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.     

Strong Convergence for a Countable Family of Total Quasi-φ-asymptotically Nonexpansive Nonself Mappings in Banach Space

The purpose of this article is to introduce a class of total quasi-φ-asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this article extend and improve the corresponding results of many authors.     

An explicit Berry-Esséen bound for uniformly expanding maps on the interval

For uniformly expanding maps on the interval, analogous versions of the Berry-Esséen theorem are known but only with an unexplicit upper bound in O(1/\(\sqrt n \)) without any constants being specified. In this paper, we use the recent complex cone technique to prove an explicit Berry-Essén estimate with a reasonable constant for these maps. Our method is not limited to maps on the interval however, and should apply to many situations.     

On uniformly Gâteaux smooth C (n)-smooth norms on separable Banach spaces

Every separable Banach space with C ⁽ⁿ⁾-smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and C ⁽ⁿ⁾-smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.     

Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings

Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x^∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x^∗)∈J(x−x^∗) such that

〈Tx−x^∗,j(x−x^∗)〉?‖x−x^∗‖2−Φ(‖x−x^∗‖).     

Certain subclasses of uniformly convex functions of order α and type β with varying arguments

In this paper, we define a new subclass of k-uniformly convex functions order α type β with varying argument of coefficients and obtain coefficient estimates. Further we investigate extreme points, growth and distortion bounds, radii of starlikeness and convexity and modified Hadamard products.     

Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE

We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs.     

An extension of Levin–Stečkin’s theorem to uniformly convex and superquadratic functions

Aequationes mathematicae - In this paper, some integral inequalities for uniformly convex functions are studied by using unordered submajorization for cumulative functions. Strongly convex...     

Hölder continuity of solutions of an elliptic equation uniformly degenerating on part of the domain

We consider a second-order divergence elliptic equation in a domain D divided by a hyperplane in two parts. The equation is uniformly elliptic in one of these parts and is uniformly degenerate with respect to a small parameter ? in the other. We show that each solution is Hölder continuous in D with Hölder exponent independent of ?.     

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.