International Journal Of Nonlinear Analysis And Applications
Volume:4 Issue: 1, Summer - Autumn 2013

A new class of function spaces on domains (i.e., open and connected subsets) of Rd, by means of the asymptotic behavior of modulations of functions and distributions, is de ned. This class contains the classes of Lebesgue spaces and modulation spaces. Main properties of this class are studied, its applications in the study of function spaces and its relations to classical function spaces are discussed.

We provide necessary and sucient conditions for -conditional as- ymptotic stability of the solution of a linear matrix Lyapunov system and sucient conditions for -conditional asymptotic stability of the solution of a rst order non-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).

In this paper, we prove that an implicit iterative process with er- rors converges strongly to a common xed point for a nite family of generalized asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results unify, improve and generalize the correspond- ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] and many others.

In this paper we study properties of symbols such that these belong to class of symbols sitting inside Sm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operators plays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudo differential operators for which define base on this class of symbols. Also we consider maximal and minimal operators of M−hypoelliptic pseudo differential operators and we express some results about these operators.

We discuss the existence of a positive solution to the in nite semipositone problem 􀀀
u = au 􀀀 bu 􀀀 f(u) 􀀀cu; x 2; u = 0; x 2 @; where
is the Laplacian operator, > 1, 2 (0; 1), a; b and c are positive constants, is a bounded domain in RN with smooth boundary @, and f: [0;1)! R is a continuous function such that f(u)! 1 as u! 1. Also we assume that there exist A > 0 and > 1 such that f(s)  As, for all s  0.. We obtain our result via the method of sub- and supersolutions.

In this paper, using the Steklov function, we introduce the generalized continuity modulus and de ne the class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.

In this paper, a modi ed version of LLL algorithm, which is a an algorithm with output-sensitive complexity, is presented to convert a given Grobner basis with respect to a speci c order of a polynomial ideal I in arbitrary dimensions to a Grobner basis of I with respect to another term order. Also a comparison with the FGLM conversion and Buchberger method is considered.

Let A be a Banach algebra,  be continuous homomorphism on A with (A) = A. The bounded linear map D: A! A is 􀀀derivation, if D(ab) = D(a)
(b) + (a)
D(b) (a; b 2 A): We say that A is -weakly amenable, when for each bounded derivation D: A! A, there exists a 2 A such that D(a) = (a)
a 􀀀 a
(a). For a commutative Banach algebra A, we show A is 􀀀weakly amenable if and only if every 􀀀derivation from A into a 􀀀symmetric Banach A􀀀bimodule X is zero. Also, we show that a commutative Banach algebra A is 􀀀weakly amenable if and only if A# is #􀀀weakly amenable, where #(a +) = (a) +.