Sur la dérivation k-pseudo-symétrique des fonctions numériques
Sull'e q u a zio n e funzionale
A wide class of partial functional equations (all generalizing in a quite natural way the classical recurrence relation for the -function), is considered in § 1, in order to give an existence and unicity theorem for the solution of each of them, provided this solution be a partially lg-convex one. Further, in § 2 is sketched a straightforward method of resolution for an interesting subclass of such a class of equations, only involving simple techniques of finite differences calculus.
On the k-pseudo-symmetrical approximate differentiability
Su talune condizioni di derivabilità applicabili ad insiemi di misura nulla
On assigne une nouvelle définition de presque absolue continuité, applicable à des ensembles de mesure nulle, et on en étudie quelque aspect. On la compare après avec une autre condition de dérivabilité presque partout, qui généralise elle aussi une condition auparavant donnée par B. Pettineo: on montre ainsi qu'entre eux subsiste, même dans la formulation étendue, une substantielle équivalence.
Su di un metodo iterativo concernente funzioni speciali
A wide extension is given of the iterative method applied in [6] to the resolution of a remarkable class of functional equations. This stresses the possibility of dealing with characterizations of some special functions (e.g. the Euler's one) by means of a “fixed point theorem” approach. An application to the above function is shown at the end.
A condition on null sets for the approximate differentiability
Si fornisce un'estensione del concetto di quasi assoluta continuità secondo Khintchine [1] e si mostra come una siffatta estensione consenta di assegnare, anche su di un insieme di L-misura nulla, una condizione caratteristica per la derivabilità approssimata quasi ovunque di una funzione reale di variabile reale.
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