the main goal of this paper is the study of the generalized hyers-ulam stability of the following functionalequation f (2x  y)  f (2x  y)  (n 1)(n  2)(n  3) f ( y)  2n2 f (x  y)  f (x  y)  6 f (x) where n  1,2,3,4 , in non–archimedean spaces, by using direct and fixed point methods.

We verify that the $p$-integrable Teichmüller space $T_{p}$ admits canonical complex Banach manifold structure for any $p \geq 1$. Moreover, we characterize a quasisymmetric homeomorphism corresponding to an element of in terms $p$-Besov $p>1$.

Non-epithelial, benign extracranial neurogenic tumors of the nasal cavities are reported in the literature with extreme rarity. These tumors differ from the more common congenital gliomas, encephaloceles, etc. in that they sometimes are detached from the brain tissues. These tumors have intracranial origins. They are congenital or acquired and may involve any of the nerves inside the nose....

We consider the problem of learning to optimize an unknown MDP M = (S,A, R, P ). S = {1, .., S} is the state space, A = {1, .., A} is the action space. In each timestep t = 1, 2, .. the agent observes a state st ∈ S, selects an action at ∈ A, receives a reward rt ∼ R(st, at) ∈ [0, 1] and transitions to a new state st+1 ∼ P (st, at). We define all random variables with respect to a probability s...

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

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...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...