Chmieliński has proved in the paper [4] the superstability of the generalized orthogonality equation |〈 f (x), f (y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmieliński by proving a theorem: Let Dn be a suitable subset of Rn. If a function f : Dn → Rn satisfies the inequality ||〈 f (x), f (y)〉|− |〈x,y〉|| ≤ φ(x,y) for an appropriate control function φ(x,y) and for all x,y ∈ Dn, ...

Root-class residuality of free product of root-class residual groups is demonstrated. A sufficient condition for root-class residuality of generalized free product G of groups A and B amalgamating subgroups H and K through the isomorphism φ is derived. For the particular case when A = B, H = K and φ is the identity mapping, it is shown that group G is root-class residual if and only if A is roo...

Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of lp distance measures, researchers were motivated to use them in almost every clustering process. Beside lp distance measures, there exist several distance measures. Sargent introduced a special type of distance measuresm(φ) and n(φ) which is closely r...

In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...

The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function φ(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann-Gibbs form with the exponential function replaced by a deformed exponential fun...

where fn : E × E → R, f : E × E → R, φn : E × E → R ∪ {∞}, φ : E × E → R ∪ {∞}. The aim of this paper is to give suitable conditions on the convergence of (fn)n to f and (φn)n to φ in order to obtain a convergence result for the solutions of (1.1)n to solutions of (1.2). This study was motivated by the increasing interest in the topic of generalized quasi-variational inequalites (in short g.q.v...

We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice of noncrossing partitions associated to the corresponding finite real reflection group. 1. The result Let Φ be a finite root system spanning an n-dimensional Euclidean space V with corresponding finite reflec...