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Fractals, 2012
The methodology of fractal sets generates new procedures for the analysis of functions whose graphs have a complex geometric structure. In the present paper, a method for the definition of fractal functions is described. The new mappings are perturbed versions of classical bases as Legendre polynomials, etc.
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The methodology of fractal sets generates new procedures for the analysis of functions whose graphs have a complex geometric structure. In the present paper, a method for the definition of fractal functions is described. The new mappings are perturbed versions of classical bases as Legendre polynomials, etc.
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On the LP space of observables
Fuzzy Sets and Systems, 1999The author studies the subspace \(L^p\) of observables in fuzzy set considerations. The main result states that the subspace \(L^p\) considered with a suitable pseudometric is complete.
Beloslav Riečan, Beloslav Riečan
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2018
The notion of convex function is more stringent than that of continuous function. It is the source of many interesting inequalities in real analysis.
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The notion of convex function is more stringent than that of continuous function. It is the source of many interesting inequalities in real analysis.
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1989
Before discussing an important special class of measurable functions we prove a fundamental inequality, known as Holder’s inequality. There are two variants, one for sums and one for integrals. The original variant for integrals of continuous functions or Riemann integrable functions was extended to measurable functions without additional difficulties.
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Before discussing an important special class of measurable functions we prove a fundamental inequality, known as Holder’s inequality. There are two variants, one for sums and one for integrals. The original variant for integrals of continuous functions or Riemann integrable functions was extended to measurable functions without additional difficulties.
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Fuzzy Sets and Systems, 2014
In the framework of the pseudo-analysis the classical L^p space is generalized and there are proved important properties of introduced space. Three types of convergence of sequences of measurable functions are considered in this space. The inequalities for integrals based on pseudo-integral have been recently proposed as the Holder, Minkowski and ...
Pap, Endre +2 more
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In the framework of the pseudo-analysis the classical L^p space is generalized and there are proved important properties of introduced space. Three types of convergence of sequences of measurable functions are considered in this space. The inequalities for integrals based on pseudo-integral have been recently proposed as the Holder, Minkowski and ...
Pap, Endre +2 more
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ON Lp -MATRICIALLY NORMED SPACES
Acta Mathematica Scientia, 2005Abstract It is proved that there is only one Lp-matricially normed space of dimension 1 and that quotient spaces of Lp-matricially normed spaces are also Lp-matricially normed spaces. Some properties of Lp-matricially normed spaces are given.
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Nullfunctions and the Lebesgue Spaces Lp
1994The integral with respect to a submodular set function allows to define norms on spaces of measurable functions. An obstacle in doing so is that (like in the σ-additive theory) there are functions, not identically zero, having norm nought. Those are the nullfunctions, we start with.
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2002
In this chapter we present three examples of continuous operators acting in L p spaces, namely: the Nemytskii superposition operator; the Fredholm linear integral operator; and the Hammerstein nonlinear integral operator. As applications we shall prove via the Leray-Schauder principle several existence results in L p for Hammerstein and Volterra ...
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In this chapter we present three examples of continuous operators acting in L p spaces, namely: the Nemytskii superposition operator; the Fredholm linear integral operator; and the Hammerstein nonlinear integral operator. As applications we shall prove via the Leray-Schauder principle several existence results in L p for Hammerstein and Volterra ...
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