Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.

Making use of the pullbacks, we reformulate the following quadratic functional equation: f x y z f x f y f z f x y f y z f z x in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperf...

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

where f∗, u∗ (or f ∗, u∗) are lower (or upper) limit functions of f and u, respectively. Assume that u is the generalized solution of the FBVP constructed by Perron’s supersolutions or subsolutions method (see [1, 6]). It is well known that, in general, the generalized solution does not satisfy (1.3). We say that a point (x0, t0) ∈ ∂Ωδ is regular if, for any bounded function f : ∂Ω→R, the gener...

The purpose of the present paper is twofold: to introduce the notion of a generalized flag in an infinite dimensional vector space V (extending the notion of a flag of subspaces in a vector space), and to give a geometric realization of homogeneous spaces of the ind–groups SL(∞), SO(∞) and Sp(∞) in terms of generalized flags. Generalized flags in V are chains of subspaces which in general canno...

Let $R$ be a prime ring with its Utumi ring of quotients $U$,  $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate} item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=...

DP-means clustering was obtained as an extension of $K$-means clustering. While it is implemented with a simple and efficient algorithm, can estimate the number clusters simultaneously. However, specifically designed for average distortion measure. Therefore, vulnerable to outliers in data, cause large maximum clusters. In this work, we extend objective function $f$-separable measures propose u...