On the Stability of the Functional Equation f(2x+y)+f(x+y2)=2f(x)f(y)f(x)+f(y)+2f(x+y)f(y-x)3f(y-x)-f(x+y)f\left( {2x + y} \right) + f\left( {{{x + y} \over 2}} \right) = {{2f\left( x \right)f\left( y \right)} \over {f\left( x \right) + f\left( y \right)}} + {{2f\left( {x + y} \right)f\left( {y - x} \right)} \over {3f\left( {y - x} \right) - f\left( {x + y} \right)}}

Connections between C(X) and C(Y), where Y is a subspace of X

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

A Note on Twists of (y^2=x^3+1)

‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with ...

Statut syntaxique des appositions en allemand du type Y, X ou Y - X ou Y(X)

connections between c(x) and c(y), where y is a subspace of x

in this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $c(x)$ and the same of $c(y)$, for some special subset $y$ of $x$. for instance, if $y=coz(f)$ for some $fin c(x)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $c(y)$ and the set of prime $z$-ideals of $c(x)$ not containing $f$. moreover, c...

Quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces

In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|