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In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality. [ABSTRACT FROM AUTHOR]

This paper considers the isometric extension problem concerning the mapping from the unit sphere S 1( E) of the normed space E into the unit sphere S 1( l ∞(Γ)). We find a condition under which an isometry from S 1( E) into S 1( l ∞(Γ)) can be linearly and isometrically extended to the whole space. Since l ∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are solved. More precisely, if E and F are two normed spaces, and if V 0: S 1( E) → S 1( F) is a surjective isometry, where c 00(Γ) ⊆ F ⊆ l ∞(Γ), then V 0 can be extended to be an isometric operator defined on the whole space. [ABSTRACT FROM AUTHOR]

In this paper, we .rst derive the representation theorem of onto isometric mappings in the unit spheres ofl1(G) type spaces, and then conclude that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide an error analysis for the multicategory support vector machine (MSVM) classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results. [ABSTRACT FROM AUTHOR]

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991). [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen’s equations in Banach modules over a unitalC*-algebra. It is applied to show the stability of universal Jensen’s equations in a Hilbert module over a unitalC*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unitalC*-algebra. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the average sigma-K width of Sobolev-Wiener classes S[sup r]sub pq]W with mixed smoothness ill L[sub q](R[sup d]) is studied for 1 < q < p < infinity, and the weak asymptotical behavior of these quantities is obtained. Keywords Sobolev-Weiner class with mixed smoothness, Average sigma-K width, Step Hyperbolic crosses [ABSTRACT FROM AUTHOR]

We study embeddings of spaces of Besov-Morrey type, [InlineMediaObject not available: see fulltext.], and obtain necessary and sufficient conditions for this. Moreover, we can also characterise the special weighted situation [InlineMediaObject not available: see fulltext.] for a Muckenhoupt $$\mathcal{A}_\infty$$ weight w, with w( x) = | x|, α > − d, as a typical example. [ABSTRACT FROM AUTHOR]

Let C be a nonempty closed convex subset of a real Banach space E. Let S: C → C be a quasi-nonexpansive mapping, let T: C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F:= { x ε C: Sx = x and Tx = x} ≠ 0. Let { x n } n≥0 be the sequence generated from an arbitrary x 0 ε C by We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence { x n } to an element of F. These extend and improve the recent results of Moore and Nnoli. [ABSTRACT FROM AUTHOR]

We present the exact values of nonsquare constants, von Neumann–Jordan constants, Jung constants, packing constants, weakly convergent sequence coefficients and normal structure coefficients in a class of reflexive Orlicz function spaces and sequence spaces equipped with Luxemburg norm and Orlicz norm. [ABSTRACT FROM AUTHOR]

Let X be an infinite–-dimensional complex Banach space and denote by ℬ( X) the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from ℬ( X) onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional φ on ℬ( X) such that either Φ( T) = cATA −1 + φ( T) I for all T, or Φ( T) = cAT*A −1 + φ( T) I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite–dimensional Hilbert space, the above similarity invariant additive functional φ is always zero. [ABSTRACT FROM AUTHOR]

A class of a posteriori parameter choice strategies for the operator version of Tikhonov regularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill–posed nonlinear equation involving a monotone operator in Banach space. [ABSTRACT FROM AUTHOR]

LetXbe a Banach space with a weak uniform normal structure andCa non-empty convex weakly compact subset ofX. Under some suitable restriction, we prove that every asymptotically regular semigroupT= {T(t) :t?¸S} of selfmappings onCsatisfyinghas a common fixed point, where WCS(X) is the weakly convergent sequence coefficient ofX, andis the exact Lipschitz constant ofT(t). [ABSTRACT FROM AUTHOR]