Investigation of a Stolarsky type Inequality for Integrals in Pseudo-Analysis
MSC 2010: 03E72, 26E50, 28E10In this paper, we prove a Stolarsky type inequality for pseudo-integrals.
MSC 2010: 03E72, 26E50, 28E10In this paper, we prove a Stolarsky type inequality for pseudo-integrals.
We work with a fixed N-tuple of quasi-arithmetic means generated by an N-tuple of continuous monotone functions (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping tend pointwise to a mapping having values on the diagonal of . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means taken on b. We effectively...
En admettant la conjecture de Dickson, nous démontrons que, pour chaque couple d’entiers et , il existe une partie infinie telle que, pour chacun des entiers et tout entier tel que , on ait où sont des nombres premiers. De même, pour chaque couple d’entiers et , il existe une partie infinie telle que, pour chacun des entiers et tout entier (nul ou non ) de l’intervalle , on ait où sont des nombres premiers et l’entier appartient à l’intervalle . La lecture non standard...
The purpose of this paper is to present Fatou type results for a sequence of Pettis integrable functions and multifunctions. We prove the non vacuity of the weak upper limit of a sequence of Pettis integrable functions taking their values in a locally convex space and we deduce a Fatou's lemma for a sequence of convex weak compact valued Pettis integrable multifunctions. We prove as well a Lebesgue theorem for a sequence of Pettis integrable multifunctions with values in the space of convex compact...
Let and be vector spaces over the same field . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation of into is called linear if and for all and . After improving and supplementing some former results on linear relations, we show that a relation of a linearly independent subset of into can be extended to a linear relation of into if and only if there exists a linear subspace of such that for all . Moreover, if generates...
For a Tychonoff space , is the lattice-ordered group (-group) of real-valued continuous functions on , and is the sub--group of bounded functions. A property that might have is (AP) whenever is a divisible sub--group of , containing the constant function 1, and separating points from closed sets in , then any function in can be approximated uniformly over by functions which are locally in . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...
The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the case have a Denjoy-Carleman counterpart.
We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized vector bundle homomorphisms and, based on this, provide a definition of tangent map for such generalized functions.
Several mean value theorems for higher order divided differences and approximate Peano derivatives are proved.