@article {
author = {Mehboodi, Soodeh and Hooshmand, Mohammad},
title = {Analytic differenceability of functions},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {3},
number = {1},
pages = {1-12},
year = {2021},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.680048},
abstract = {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).},
keywords = {Bernoulli and Euler polynomials,Bernoulli and Euler numbers,Analytic summability},
url = {http://www.macajournal.com/article_680048.html},
eprint = {http://www.macajournal.com/article_680048_f8dc878765ad98f0ebdf44b27b6ff0a5.pdf}
}
@article {
author = {Rassias, John and Sathya, Elumalai and Arunkumar, Mohan},
title = {Generalized Ulam-Hyers stability of an alternate additive-quadratic-quartic functional equation in fuzzy Banach spaces},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {3},
number = {1},
pages = {13-31},
year = {2021},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.680135},
abstract = {In this paper, we obtain and establish the generalized Ulam-Hyers stability of an additive-quadratic-quartic functional equation in fuzzy Banach spaces.},
keywords = {Additive functional equations,Quadratic functional equations,quartic functional equations,mixed type functional equations,Ulam-Hyers-Rassias stability,Fuzzy Banach space},
url = {http://www.macajournal.com/article_680135.html},
eprint = {http://www.macajournal.com/article_680135_d60cd51f1af4dbd4cd12706d2b3dac94.pdf}
}
@article {
author = {Mousavi, Lida and Hosseini, Sedigheh},
title = {Some results on disjointness preserving Fredholm operators between certain Banach function algebras},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {3},
number = {1},
pages = {32-39},
year = {2021},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1924698.1002},
abstract = {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.},
keywords = {Disjointness preserving,Weighted composition,Fredholm},
url = {http://www.macajournal.com/article_681367.html},
eprint = {http://www.macajournal.com/article_681367_92f3f2b3a35ecdaec6c83cde90844811.pdf}
}
@article {
author = {Paykan, Kamal},
title = {Weakly principally quasi-Baer rings and generalized triangular matrix rings},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {3},
number = {1},
pages = {39-45},
year = {2021},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1925653.1004},
abstract = {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.},
keywords = {Generalized triangular matrix ring,Annihilator,Quasi-Baer,Weakly principally quasi-Baer,Semicentral idempotent},
url = {http://www.macajournal.com/article_681125.html},
eprint = {http://www.macajournal.com/article_681125_83625f3e4916f6dc8ea18a5541568207.pdf}
}
@article {
author = {Fabiano, Nicola},
title = {A proof of the Cauchy--Schwarz inequality from the change of reference frame},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {3},
number = {1},
pages = {46-47},
year = {2021},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1927475.1005},
abstract = {Inspired by [1] a proof of the Cauchy--Schwarz inequality is given by considering the transformation between two different inertial reference frames.},
keywords = {Cauchy--Schwarz inequality,reference frame},
url = {http://www.macajournal.com/article_681376.html},
eprint = {http://www.macajournal.com/article_681376_563a8d584d85c8965f309710199bea4e.pdf}
}
@article {
author = {Subramani, Karthikeyan and Park, Choonkil and Rassias, John},
title = {Stability of quartic functional equation in paranormed spaces},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {3},
number = {1},
pages = {48-58},
year = {2021},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1924046.1001},
abstract = {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.},
keywords = {paranormed space,quartic functional equation,Ulam-Hyers stability,fixed point method},
url = {http://www.macajournal.com/article_680651.html},
eprint = {http://www.macajournal.com/article_680651_4b4d55ea22b5b3dc10901cdc23cdf79b.pdf}
}