We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introd...

Although derivations from Banach algebras to particular coefficient modules have been much studied, interest has usually focused on the existence or otherwise of non-trivial bounded derivations, rather than their characterisation. Even in the special case of derivations from a commutative Banach algebra to its dual (as in [2] or [5] for example), there are comparatively few examples where the s...

we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...

In this work, the definition of first and second types multiplicative Chebyshev differential equations is given solutions these are investigated with help power series. Also, properties type polynomials proved. Finally, studies supported numerical examples.