Abstract
In the paper we present some properties of functions which are ϱ-upper continuous in O’Malley’s sense. Connections with the standard ϱ-upper continuous functions are studied and the maximal additive class and the maximal multiplicative class for this family of functions are described.
References
[1] Borsík, J.—Holos, J.: Some properties of porouscontinuous functions, Math. Slovaca 64 (2014), 741–750.10.2478/s12175-014-0237-3Search in Google Scholar
[2] Bruckner, A. M.: Differentation of Real Functions. Lecture Notes in Mathematics, Vol. 659, Springer-Verlag Berlin Heidelberg New York, 1978.Search in Google Scholar
[3] 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/conm/042/807973Search in Google Scholar
[4] Kowalczyk, S.: On preponderantly continuous functions, Pr. Nauk. Akad. Jana Długosza Częst. Mat. XIV (2009), 75–86.Search in Google Scholar
[5] Kowalczyk, S.—Nowakowska, K.: A note on ϱ-upper continuous functions, Tatra Mt. Math. Publ. 44 (2009), 153–158.10.2478/v10127-009-0055-0Search in Google Scholar
[6] Kowalczyk, S.—Nowakowska, K.: Maximal classes for ϱ-upper continuous functions, J. Appl. Anal. 19 (2013), 69–89.10.1515/jaa-2013-0005Search in Google Scholar
[7] Kowalczyk, S.—Nowakowska, K.: A note on the [0]-lower continuous functions, Tatra Mt. Math. Publ. 58 (2014), 111–128.10.2478/tmmp-2014-0010Search in Google Scholar
[8] Kowalczyk, S.—Nowakowska, K.: Maximal classes for the family of [λ,ϱ]-continuous functions, Real Anal. Exchange 36 (2010/11), 307–324.10.14321/realanalexch.36.2.0307Search in Google Scholar
[9] O’Malley, R. J.: Note about preponderantly continuous functions, Revue Roumanie Math. Pureed Appl. 21 (1976), 335–336.Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Some results in local Hilbert algebras
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- The first law of cubology for the Rubik’s Revenge
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- Systems of conditionally independent sets
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- Some remarks on formal power series and formal Laurent series
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- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
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- A characterization of holomorphic bivariate functions of bounded index
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- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
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Articles in the same Issue
- Some results in local Hilbert algebras
- A note on residuated po-groupoids and lattices with antitone involutions
- The first law of cubology for the Rubik’s Revenge
- Conditional associativity in orthomodular lattices
- A monotonicity property for generalized Fibonacci sequences
- Systems of conditionally independent sets
- On the k-th order lfsr sequence with public key cryptosystems
- On parametric spaces of bicentric quadrilaterals
- Character sums with an explicit evaluation
- Some remarks on formal power series and formal Laurent series
- The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
- On prime and semiprime generalized hyperaction of hypermonoid
- On O’Malley ϱ-upper continuous functions
- Uniqueness theorems for finitely additive probabilities on quantum structures
- Some results on differential-difference analogues of Brück conjecture
- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
- On support, separation and decomposition theorems for t-Wright-concave functions
- A characterization of holomorphic bivariate functions of bounded index
- Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
- A comparison of two tests in multivariate models
- Modelling prescription behaviour of general practitioners
- Characterization of congruence lattices of principal p-algebras