The aim of this paper is to introduce and solve the following pradical functional equation related Drygas mappings f(?(p&x^p+ y^p ))+f(?(p&x^p+ ))=2f(x)+f(y)+f(-y),x,y ?R, where f a mapping from R into vector space X p ? 3 an odd natural number. Using analogue version Brzd?k’s fixed point theorem [14], we establish some hyperstability results for considered in non-Archimedean Banach spa...

Consider a set P of m points in R. Given a polynomial f ∈ R[x1, . . . , xd], we define the zero set of f to be Z(f) = {p ∈ R | f(p) = 0}. For any r > 1, we say that f ∈ R[x1, . . . , xd] is an r-partitioning polynomial for P if every connected component of R \ Z(f) contains at most m/r points of P.1 Notice that there is no restriction on the number of points of P that lie in Z(f). Figure 1 depi...

The stellar dynamic models considered here deal with triples ( $$f,\;\rho ,\;U$$ ) of three functions: the distribution function $$f = f(r,u)$$ , local density $$\rho \rho (r)$$ and Newtonian potential $$U U(r)$$ where $$r: \left| x \right|$$ $$u: {v} $$(x,{v}) \in {{\mathbb{R}}^{3}} \times {{\mathbb{R}}^{3}}$$ are space-velocity coordinates), $$f$$ is a $$q$$ energy $$E U(r) + \frac{{{{u}^{2}}...

We consider an operator equation) (, A R f f Au ∈ = , (1) where is the linear continuous operator between real Hilbert spaces H and F. In general our problem is ill-posed: the range R(A) may be non-closed, the kernel N(A) may be non-trivial. We suppose that instead of exact right-hand side f we have only an approximation) , (F H L A ∈ F f ∈ δ , δ δ ≤ − f f. To get regularized solution of the eq...

We establish, for $1<p<\\infty$, higher order $\\mathcal{S}^{p}$-differentiability results of the function $\\varphi \\colon t\\in \\mathbb{R} \\mapsto f(A+tK) - f(A)$ selfadjoint operators $A$ and $K$ on a separable Hilbert space $\\mathcal{H}$ with element Schatten class $\\mathcal{S}^{p}(\\mathcal{H})$ $f$ $n$-times differentiable $\\mathbb{R}$. prove that if either $f^{(n)}$ are bound...

Humans can r e c o v e r t h e shape o f a s u r f a c e f r o m i t s image b o u n d a r y . The a u t h o r s have p r e s e n t e d a new a p p r o a c h t o shape f r o m b o u n d a r y [ 4 ] . I t i n c l u d e s t h r e e p o i n t s : t h e l i n e o f c u r v a t u r e (LOC) r e g u l a r i t y , a n a l g o r i t h m f o r c o n s t r u c t i n g LOC net f r o m b o u n d a r y , and...