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Extension of convex semi-Lipschitz functions on quasi-metric linear spaces

3 years ago

Abstract In this paper one shows that a convex semi-Lipschitz functions defined on a convex subset of a quasi-metric linear…

On the extremal semi-Lipschitz function

3 years ago

Abstract The extremal elements of the unit balls of Banach spaces play an important role in the study of the…

A Phelps type result for spaces with asymmetric norms

3 years ago

Abstract If \((X,||\cdot|)\) is a linear space with asymmetric norm and \(Y\) is a \(X\), for every \(f\in Y_{+}^{\ast}\) (the…

On the uniqueness of extension and unique best approximation in the dual of an asymmetric normed linear space

3 years ago

Abstract A well known result of R. R. Phelps (1960) asserts that in order that every linear continuous functional, defined…

On the extension of semi-Lipschitz functions on asymmetric normed spaces

3 years ago

Abstract Extension theorems for semi-Lipschitz functions and some proper- ties of these extensions useful in approximation problems are presented. As…

Best approximation in spaces with asymmetric norm

3 years ago

Abstract In this paper we shall present some results on spaces with asymmetric seminorms, with emphasis on best approximation problems…

On the converses of the reduction principle in inner product spaces

3 years ago

Abstract Let \(H\) be an inner product space, \(X\) a complete subspace of \(H\), and \(Y\) a closed subspace of…

Best uniform approximation of semi-Lipschitz function by extension

3 years ago

Abstract In this paper we consider the problem of best uniform approximation of a real valued semi-Lipschitz function \(F\) defined…

On a theorem of Baire about lower semi-continuous functions

3 years ago

Abstract A theorem of Baire concerning the approximation of lower semicontinuous real valued functions defined on a metric space, by…

Extensions of semi-Hölder real valued functions on a quasi-metric space

3 years ago

Abstract In this note, the semi-Holder real valued functions on a quasi-metric (asymmetric metric) space are defined. An extension theorem…

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