Gâteaux differentiable functions are somewhere Fréchet differentiable
General Fritz Carlson's type inequality for Sugeno integrals.
Generalization of an inequality for integral transforms with kernel and related results.
Generalization of integral inequalities for functions whose modulus of derivatives are convex.
Generalization of Stolarsky type means.
Generalizations of a class of inequalities for products.
Generalized abstracted mean values.
Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule
Generalized iterated function systems, multifunctions and Cantor sets
Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.
Generalized weighted quasi-arithmetic means and the Kolmogorov-Nagumo theorem
A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions , k ≥ 2, denoted by , is considered. Some properties of , including “associativity” assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For a sequence of...
Generators for algebras dense in -spaces
For various -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...
Giving lectures on nonstandard analysis. (Lire l'analyse non standard.)
Globale und lokale Erzeugendenanzahl im Reellen.
Graded sets, points and numbers.
The basic tool considered in this paper is the so-called graded set, defined on the analogy of the family of α-cuts of a fuzzy set. It is also considered the corresponding extensions of the concepts of a point and of a real number (again on the analogy of the fuzzy case). These new graded concepts avoid the disadvantages pointed out by Gerla (for the fuzzy points) and by Kaleva and Seikkala (for the convergence of sequences of fuzzy numbers).