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Abstract  

Let (X, d) be a quasi-metric space and (Y, q) be a quasi-normed linear space. We show that the normed cone of semi-Lipschitz functions from (X, d) to (Y, q) that vanish at a point x 0X, is balanced. Moreover, it is complete in the sense of D. Doitchinov whenever (Y, q) is a biBanach space.

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Abstract  

This paper deals with three classes of functions of great importance in analysis and its applications. We construct a family of Hlder functions in the closed unit interval having two continuous parameters. Those functions are not of bounded variation for any pair of values of the Hlder constant and exponent. The construction depends on a change of variables given by a Lipschitz function with constant equal to 1. Several questions related to the concepts of genericity, surjectivity and deformability are posed at the end.

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Lipschitz functions in ℝ N , CECM Preprint 95:048, 1995. Wang, X. , Fine and topological properties of subdifferentials, CECM Preprint 99:134, 1999. Yang, X. Q

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). [8] Macías , R. A. , Segovia , C. 1979 Lipschitz functions on spaces of homogeneous type Adv. in Math. 33 257 – 270 10.1016/0001-8708(79)90012-4 . [9

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. Math. , 36 ( 2010 ), no. 4 , 299 – 319 . [10] Nagy , K. , Approximation by Nörlund means of double Walsh–Fourier series for Lipschitz functions , Math

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460 Romaguera, S. and Sanchis, M., Semi-Lipschitz functions and best approximation in quasi-metric spaces, J. Approx. Theory 103 (2000), 292-301. MR 2001a :54023

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egovia , C. , Lipschitz functions on spaces of homogeneous type , Adv. Math. , 33 ( 1979 ), 257 – 270 . [27] M acManus , P. and P érez , C. , Generalized Poincaré

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] K . Nagy . Approximation by Nörlund means of quadratical partial sums of double Walsh–Fourier series . Anal. Math , 36 ( 4 ): 299 – 319 , 2010 . [22] K . Nagy . Approximation by Nörlund means of double Walsh–Fourier series for Lipschitz

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