International Journal Of Nonlinear Analysis And Applications
Volume:5 Issue: 1, Summer - Autumn 2014

We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arens regular Banach algebras such that tensor product becomes irregular, where is tensor norm. We illustrate injective tensor product, does not preserve bounded approximate identity and it is not algebra norm.

We study an interesting class of Banach function algebras of in nitely di erentiable functions on perfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, called Lipschitz algebras of in nitely di erentiable functions and denoted by Lip(X;M;), where X is a perfect, compact plane set, M = fMng1n =0 is a sequence of positive numbers such that M0 = 1 and (m+n)! Mm+n  (m! Mm)(n! Mn) for m; n 2 N [f0g and 2 (0; 1]. Let d = lim sup(n! Mn) 1 n and Xd = fz 2 C: dist(z;X)  dg. Let LipP;d(X;M;)[LipR;d(X;M;)] be the subalgebra of all f 2 Lip(X;M;) that can be approximated by the restriction to Xd of polynomials [rational functions with poles o Xd]. We show that the maximal ideal space of LipP;d(X;M;) is cXd, the polynomially convex hull of Xd, and the maximal ideal space of LipR;d(X;M;) is Xd, for certain compact plane sets.. Using some formulae from combinatorial analysis, we nd the maximal ideal space of certain subalgebras of Lipschitz algebras of in nitely di erentiable functions.

Let A be a Banach ternary algebra over a scalar eld R or C and X be a Banach ternary A module. Let ; " and  be linear mappings on A, a linear mapping D: (A; []A)! (X; []X) is called a ternary (; "; )-derivation, ifD([xyz]A) = [D(x)" (y)(z)]X + [(x)D(y)(z)]X + [(x)" (y)D(z)]X for all x; y; z 2 A. In this paper, we investigate ternary (; "; )-derivation on Banach ternary algebras, associated with the following functional equationf(x + y + z4) + f(3x 􀀀 y 􀀀 4z4) + f(4x + 3z 4) = 2f(x): Moreover, we prove the generalized Ulam{Hyers stability of ternary (; "; )-derivations on Banach ternary algebras.

The xed point result in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal [Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms of anticipative contractions over the associated (standard) metric space.

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partially ordered sets. Some basic properties on these new de ned sets are studied and some examples for clarifying are given.

In this paper, we introduce a new class of set-valued contractions and obtain a xed point theorem for such mappings in complete metric spaces. Our main result generalizes and improves many well- known xed point theorems in the literature.

By using Euler-Maclaurin''s summation formula and the way of real analysis, a more accurate multiple Hilbert-type inequality and the equivalent form are given. We also prove that the same constant factor in the equivalent inequalities is the best possible.

In this paper, by using the way of weight coecients and technique of real analysis, a multidimensional discrete Hilbert-type inequality with a best possible constant factor is given. The equivalent form, the operator expression with the norm are considered.

A companion of Ostrowski''s inequality for functions of bounded variation and applications re given.

In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy''s inequality in two and three dimensions