On the family of [λ,ρ]-continuous functions

Katarzyna Nowakowska

doi:10.2478/v10127-009-0053-2

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On the family of [λ,ρ]-continuous functions

Tatra Mountains Mathematical Publications

Volume 44 (2009): Issue 1 (December 2009)

By: Katarzyna Nowakowska

Open Access

|Nov 2012

Abstract

In this paper, we introduce the class of [λ, ρ] -continuous functions. First, we investigate some relations between the classes of [ λ₁, ρ₁] and [λ₂,ρ₂] -continuous functions for different pairs [λ₁,ρ₁] , [λ₂,ρ₂]. Next, we give an equivalent condition for a function in order that it will belong to the discussed class.

References

[1] BRUCKNER, A. M.: Differentiation of Real Functions. Lecture Notes in Math., Vol. 659, Springer-Verlag, New York, 1978.10.1007/BFb0069821
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[2] BRUCKNER, A. M.-O'MALLEY, R. J.-THOMSON, B. S.: Path derivatives: a unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), 97-125.10.1090/S0002-9947-1984-0735410-1
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[3] KOWALCZYK, S.: Algebraic Properties of Families of Preponderantly Continuous Functions in the Sense of Denjoy O'Malley and Grande. Ph.D. Thesis, Lodz, 1994. (In Polish)
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Articles in this issue

DOI: https://doi.org/10.2478/v10127-009-0053-2 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 129 - 138

Published on: Nov 12, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

density of a set at a point,

continuous functions,

approximately continuous functions,

path continuity.

Related subjects:

Mathematics,

General mathematics

© 2012 Katarzyna Nowakowska, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 44 (2009): Issue 1 (December 2009)