In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...

Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.

We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is this semiring and prove when implies the commutativity of $S$.

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.