Analytic differenceability of functions Soodeh Mehboodi Zand Institute of Higher Education, Shiraz, Iran. author Mohammad Hooshmand Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran. author text article 2021 eng 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). Mathematical Analysis and its Contemporary Applications A.I.A University Publishing Group. 2716-9890 3 v. 1 no. 2021 1 12 http://www.macajournal.com/article_680048_f8dc878765ad98f0ebdf44b27b6ff0a5.pdf dx.doi.org/10.30495/maca.2021.680048 Generalized Ulam-Hyers stability of an alternate additive-quadratic-quartic functional equation in fuzzy Banach spaces John Rassias Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str. Aghia Paraskevi, Athens 15342, Greece. author Elumalai Sathya Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai - 606 603, TamilNadu, India. author Mohan Arunkumar Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India. author text article 2021 eng In this paper, we obtain and establish the generalized Ulam-Hyers stability of an additive-quadratic-quartic functional equation in fuzzy Banach spaces. Mathematical Analysis and its Contemporary Applications A.I.A University Publishing Group. 2716-9890 3 v. 1 no. 2021 13 31 http://www.macajournal.com/article_680135_d60cd51f1af4dbd4cd12706d2b3dac94.pdf dx.doi.org/10.30495/maca.2021.680135 Some results on disjointness preserving Fredholm operators between certain Banach function algebras Lida Mousavi Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran author Sedigheh Hosseini Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. author text article 2021 eng 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. Mathematical Analysis and its Contemporary Applications A.I.A University Publishing Group. 2716-9890 3 v. 1 no. 2021 32 39 http://www.macajournal.com/article_681367_92f3f2b3a35ecdaec6c83cde90844811.pdf dx.doi.org/10.30495/maca.2021.1924698.1002 Weakly principally quasi-Baer rings and generalized triangular matrix rings Kamal Paykan Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran author text article 2021 eng 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. Mathematical Analysis and its Contemporary Applications A.I.A University Publishing Group. 2716-9890 3 v. 1 no. 2021 39 45 http://www.macajournal.com/article_681125_83625f3e4916f6dc8ea18a5541568207.pdf dx.doi.org/10.30495/maca.2021.1925653.1004 A proof of the Cauchy--Schwarz inequality from the change of reference frame Nicola Fabiano Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12--14, 11351 Belgrade, Serbia author text article 2021 eng Inspired by  a proof of the Cauchy--Schwarz inequality is given by considering the transformation between two different inertial reference frames. Mathematical Analysis and its Contemporary Applications A.I.A University Publishing Group. 2716-9890 3 v. 1 no. 2021 46 47 http://www.macajournal.com/article_681376_563a8d584d85c8965f309710199bea4e.pdf dx.doi.org/10.30495/maca.2021.1927475.1005 Stability of quartic functional equation in paranormed spaces Karthikeyan Subramani Department of Mathematics R.M.K. Engineering College Kavarapettai author Choonkil Park Department of Mathematics, Hanyang University, Republic of Korea author John Rassias Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str. Aghia Paraskevi, Athens 15342, Greece. author text article 2021 eng 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. Mathematical Analysis and its Contemporary Applications A.I.A University Publishing Group. 2716-9890 3 v. 1 no. 2021 48 58 http://www.macajournal.com/article_680651_4b4d55ea22b5b3dc10901cdc23cdf79b.pdf dx.doi.org/10.30495/maca.2021.1924046.1001