Journal of Mathematical Analysis and its Contemporary Applications
Volume:3 Issue: 1, Winter 2021

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 Σ∞n=0cnEn(z).

In this paper, we obtain and establish the generalized Ulam-Hyers stability of an additive-quadratic-quartic functional equation in fuzzy Banach spaces.

For two algebras $A$ and $B$, a linear map $T : A lo B$ is disjointness preserving if $x cdot y = 0$ implies $Tx cdot Ty = 0$ for all $x, y in A$ and is said Fredholm if dim(ker($T$)) i.e. the  nullity of $T$ and codim($T(E)$) i.e. the corank of $T$ are finite. We develop some results of  Fredholm linear disjointness preserving operators from $C_0(X)$ into $C_0(Y)$ for locally compact  Hausdorff spaces $X$ and $Y $in cite{JW28}, into regular Banach function algebras. In particular,  we consider weighted composition Fredholm operators as a typical example of disjointness preserving  Fredholm operators on certain regular Banach function algebras.

A ring $R$ is called weakly principally quasi-Baer or simply (weakly p.q.-Baer) if the right annihilator of a principal right ideal is right $s$-unital by right semicentral idempotents. In this paper, we characterize when a generalized triangular matrix ring is a weakly p.q.-Baer ring.

Inspired by [1] a proof of the Cauchy--Schwarz inequality is given by considering the transformation between two different inertial reference frames.

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.