‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitr...

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

The purpose of this chapter is to write about Quot and Hilbert functors and to prove that these are algebraic spaces provided certain technical conditions are satisfied. In this chapter we will discuss this in the setting of algebraic space. A reference is Grothendieck’s lectures, see [Gro95a], [Gro95b], [Gro95e], [Gro95f], [Gro95c], and [Gro95d]. Another reference is the paper [OS03]; this pap...

We study the Hilbert polynomials of non-standard graded algebras R, that are finitely generated on generators not all of degree one. Given an expression P (R, t) = a(t)/(1 − t) for the Poincaré series of R as a rational function, we study for 0 ≤ i ≤ l the graded subspaces ⊕kRkl+i (which we denote R[l; i]) of R, in particular their Poincaré series and Hilbert functions. For example, we prove th...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.

A topological machine is a topo |ogized quas i -machine of G i n s b u r g and is defined by two cont inuous funct ions f and g, T ~ X x S ~ X , the s ta tet rans i t ion funct ion and the output funct ion, respect ively, where .X is a nonvoid T2-space, the state space, S and T are two topological semigroups , the i n p u t semigroup and the ou tpu t semigroup, respect ively, such tha t f (x, s...

Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all  continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}