On the Extensions Preserving the Shape of a Semi-Hölder Function

Abstract

We present some results concerning the extension of a semi-Hölder real-valued function defined on a subset of a quasi-metric space, preserving some shape properties: the smallest semi-Hölder constant, the radiantness and the global minimum (maximum) of the extended function.

Authors

Costică Mustăța
”Tiberiu Popoviciu” Institute of Numerical Analysis Cluj-Napoca, Romanian Academy

Keywords

Quasi-metric space; semi-Holder function; radiant function

References

See the expanding block below.

Paper coordinates

Mustăţa, C.,  On the extensions preserving the shape of a semi-Hölder function, Results. Math. 63 (2013), 425–433.
doi: 10.1007/s00025-011-0206-x

PDF

?

About this paper

Journal

Results in Mathematics

Publisher Name

Springer

Print ISSN

1422-6383

Online ISSN

1420-9012

Google Scholar Profile

?

[1] Breckner, W.W.: Holder continuity of certain generalized convex functions. Optimization 28, 201–209 (1994)
[2] Cobzas, S.: Functional analysis in asymmetric normed spaces, arXiv:1006. 1175v1.
[3] Collins, J., Zimmer, J.: An asymmetric Arzel`a-Ascoli theorem. Topol. Appl. 154, 2312–2322 (2007)
[4] Doagooei, A.R., Mohebi, H.: Optimization of the difference of ICR functions. Nonlinear Anal. Theor. Method Appl. 71, 4493–4499 (2009)
[5] Flecther, P., Lindgren, W.F.: Quasi-uniform spaces. Dekker, New York (1982)
[6] Krein, M.G., Nudel’man, A.A.: The Markov moment problem and extremum problems, Nauka, Moscow 1973 (in Russian), English translation . American Mathematical Society, Providence (1977)
[7] Kunzi, H.-P.A.: Nonsymmetric distances and their associated topologies: about the origin of basic ideas in the area of asymmetric topology. In: Aull, C.E., Lowen, R. Handbook of the history of general topology, pp. 853–968. Kluwer Academic Publishers, Dordrecht (2001)
[8] Martinez-Legaz, J.E., Rubinov, A.M., Schaible, S.: Increasing quasi-concave coradiant functions with applications in mathematical economics. Math. Oper. Res. 61, 261–280 (2005)
[9] Matouskova, E.: Extensions of continuous and Lipschitz functions. Canad. Math. Bull. 43(2), 208–217 (2000)
[10] McShane, E.T.: Extension of range of functions. Bull. Am. Math. Soc. 40, 837–842 (1934)
[11] Mennucci, A.: On asymmetric distances, Tech. Rep. Scuola Normale Superiore, Pisa (2004)
[12] Mustata, C.: Extension of semi-Lipschitz functions on quasi-metric spaces. Rev. Anal. Num´er. Th´eor. Approx. 30, 61–67 (2001)
[13] Mustata, C.: A Phelps type theorem for spaces with asymmetric norms. Bull. Stiint¸. Univ. Baia Mare, Ser. B. Matematic˘a-Informatic˘a 18, 275–280 (2002)
[14] Mustata, C.: On the approximation of the global extremum of a semi-Lipschitz function. Mediterr. J. Math. 6, 169–180 (2009)
[15] Mustata, C.: Extensions of semi-H¨older real valued functions on a quasi-metric space. Rev. Anal. Num´er. Th´eor. Approx. 38, 164–169 (2009)
[16] Phelps, R.R.: Uniqueness of Hahn-Banach extension and unique best approximation. Trans. Am. Math. Soc. 95, 238–255 (1960)
[17] Romaguera, S., Sanchis, M.: Semi-Lipschitz functions and best approximation in quasi-metric spaces. J. Approx. Theor. 103, 292–301 (2000)
[18] Romaguera, S., Sanchis, M.: Properties of the normed cone of semi-Lipschitz functions. Acta Math. Hungar 108, 55–70 (2005)

2013

Related Posts