Mathematical Analysis and its Contemporary Applications
http://www.macajournal.com/
Mathematical Analysis and its Contemporary Applicationsendaily1Wed, 24 Feb 2021 00:00:00 +0330Wed, 24 Feb 2021 00:00:00 +0330Analytic differenceability of functions
http://www.macajournal.com/article_680048.html
Analytic summability of functions was introduced by Hooshmand in 2016. He used Bernoulli numbers and polynomials Bn(z) to define analytic summability and related analytic summand functions. Since the Bernoulli and Euler polynomials have many similarities, so it motivated us to define differenceability and introduce analytic difference function of a complex or real function by utilizing the Euler numbers and polynomials En(z). Also, we prove some criteria for analytic differenceability of analytic functions. Moreover, we observe that the analytic difference function is indeed a series of the Euler polynomials and arrive at some series convergence tests for Euler polynomial series &Sigma;&infin;n=0cnEn(z).Generalized Ulam-Hyers stability of an alternate additive-quadratic-quartic functional equation in fuzzy Banach spaces
http://www.macajournal.com/article_680135.html
In this paper, we obtain and establish the generalized Ulam-Hyers stability of an additive-quadratic-quartic functional equation in&nbsp;fuzzy Banach spaces.Some results on disjointness preserving Fredholm operators between certain Banach function algebras
http://www.macajournal.com/article_681367.html
For two algebras $\A$ and $\B$, a linear map $T : \A \lo \B$ is&nbsp;disjointness preserving if $x \cdot y = 0$ implies $Tx \cdot Ty = 0$ for all&nbsp;$x, y \in \A$ and&nbsp;is said Fredholm if dim(ker($T$)) i.e. the&nbsp; nullity of $T$ and&nbsp;codim($T(E)$) i.e. the corank of $T$ are finite. We develop some results&nbsp;of&nbsp; Fredholm linear disjointness preserving operators from $C_0(X)$ into $C_0(Y)$ for&nbsp;locally compact&nbsp; Hausdorff spaces $X$ and $Y $in \cite{JW28}, into regular Banach function algebras.&nbsp;In particular,&nbsp; we consider weighted composition Fredholm operators as a&nbsp;typical example of disjointness preserving&nbsp; Fredholm operators&nbsp;on certain regular Banach function algebras.Weakly principally quasi-Baer rings and generalized triangular matrix rings
http://www.macajournal.com/article_681125.html
A ring $R$ is called weakly&nbsp;principally quasi-Baer or simply (weakly p.q.-Baer) if the right&nbsp;annihilator of a principal right ideal is right $s$-unital by right&nbsp;semicentral idempotents. In this paper, we&nbsp;characterize when a generalized triangular matrix ring is a weakly&nbsp;p.q.-Baer ring.A proof of the Cauchy--Schwarz inequality from the change of reference frame
http://www.macajournal.com/article_681376.html
Inspired by [1] a proof of the Cauchy--Schwarz inequality is given by considering the transformation between two different inertial reference frames.Stability of quartic functional equation in paranormed spaces
http://www.macajournal.com/article_680651.html
In this paper, we prove the Ulam-Hyers stability of the following quartic functional equation in paranormed spaces using both direct and fixed point methods.