Some problems in the Calculus of Variations
Journal Title: Annales Mathematicae Silesianae - Year 2017, Vol 31, Issue
Abstract
We present some results and open problems in the Calculus of Variations.
Authors and Affiliations
Arrigo Cellina
We present some results and open problems in the Calculus of Variations.
Arrigo Cellina
Some new Ostrowski’s inequalities for functions whose nth derivatives are logarithmically convex
Some new Ostrowski’s inequalities for functions whose n-th derivative are logarithmically convex are established.
Invariant means on Banach spaces
In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.
Fixed point results satisfying rational type contractive conditions in complex valued metric spaces
The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known...
Alienation of the Jensen, Cauchy and d’Alembert equations
Let $(S,+)$ be a commutative semigroup, $\sigma : S \to S$ be an endomorphism with $\sigma^2 = id$ and let $K$ be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen eq...
Stability of functional equations in dislocated quasi-metric spaces
We present a result on the generalized Hyers–Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove...