in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

Genomics-based prediction of hybrid performance promises to boost selection gain. The main goal of our study was to investigate the relevance of additive, dominance, and epistatic effects for determining hybrid seed yield in a biparental rapeseed population. We re-analyzed 60,000 SNP array and seed yield data points from an immortalized F2 population comprised of 318 hybrids and 180 parental li...

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

Additive mapping scheme represents alternative signals of selected mapping (SLM) by linear combination of signals in time domain for peak to average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) system. It can reduce the computational complexity considerably without sacrificing PAPR reduction performances especially for the OFDM system with quadrature amplitu...

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.