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ISSN : 1226-0657
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Vol.25 No.3
Abstract
In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying <TEX>$(G([x,y</TEX><TEX>]</TEX><TEX>)-[G(x),y</TEX><TEX>]</TEX><TEX>)^n=0$</TEX> for all x, <TEX>$y{\in}I$</TEX>, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.
Abstract
In this paper, we discuss central index oriented and slowly changing function based some growth properties of composite entire functions.
Abstract
An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.
Abstract
In this paper, we solve the additive <TEX>${\rho}$</TEX>-functional equations <TEX>$$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$</TEX>, where <TEX>${\rho}$</TEX> is a fixed non-Archimedean number with <TEX>${\mid}{\rho}{\mid}$</TEX> < 1, and <TEX>$$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$</TEX>, where <TEX>${\rho}$</TEX> is a fixed non-Archimedean number with <TEX>${\mid}{\rho}{\mid}$</TEX> < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive <TEX>${\rho}$</TEX>-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.