and Applied Analysis 3 Theorem 1.2 Rassias 18 . Let X be a real normed linear space and Y a real complete normed linear space. Assume that f : X → Y is an approximately additive mapping for which there exist constants θ ≥ 0 and p, q ∈ R such that r p q / 1 and f satisfies the inequality ∥ ∥f ( x y ) − f x − f(y)∥∥ ≤ θ‖x‖p∥∥y∥∥q 1.5 for all x, y ∈ X. Then there exists a unique additive mapping L...

We complete a description of additive partition entropies. This time we do not assume I to be continous. In the process we solve a 2-cocycle functional equation for certain subsets of convex cones. 1. Introduction. We assume all definitions and results from [3]. In the current follow-up paper we drop the assumption of the continuity of the additve partition entropy. Our aim is to prove a theore...

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In this paper, we consider the following singular first order functional difference equation Δx(k) = −a(k)x(k) + λb(k)f(x(k − τ(k))), k ∈ Z where f(.) is singular at x = 0. By using a Kranoselskii fixed point theorem, we will establish the existence and multiplicity of positive periodic solutions for the above problem. The results obtained are new, and some examples are given to illustrate our ...

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are deri...