Generalized Derivative and Generalized Continuity-Reference-Cited by-同舟云学术

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Generalized Derivative and Generalized Continuity

Published:2019-11-15 Issue:1 Volume:74 Page:77-84
ISSN:1210-3195
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Kupka Ivan¹

Affiliation:

1. Faculty of Mathematics, Physics and Informatics , Comenius University , Bratislava , Slovakia

Abstract

Abstract The main objective of this article is to show that generalized differentiation can be understood as a process of comparing functions and their generalized continuity properties. We show it by working with generalized notions of derivative and continuity. The article covers wide range of types of generalized continuity.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2019-0021

Reference27 articles.

1. [1] AMBROSIO, L.—KIRCHHEIM, B.: Rectifiable sets in metric and Banach spaces,Math. Ann. 318 (2000), 527–555.10.1007/s002080000122

2. [2] AVERSA, V.—PREISS, D.: Lusin’s theorem for derivatives with respect to a continuous function, Proc. Amer. Math. Soc. 127 (1999), 3229–3235.10.1090/S0002-9939-99-05086-8

3. [3] BILET, V.—DOVGOSHEY, O.—KÜÇÜKASLAN, M.: Uniform boundedness of pretan-gent spaces, local constancy of metric valued derivatives and strong right upper porosity at a point,J. Anal. 21 (2013), 31–55.

4. [4] BORSÍK, J.: Bilateral quasicontinuity in topological spaces, Tatra Mt. Math. Publ. 28 (2004), 159–168.

5. [5] _______ On the points of bilateral quasicontinuity of functions, Real Anal. Exchange 19 (1993/1994), 529–536.10.2307/44152402

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