ORIGINAL_ARTICLE
Analytic differenceability of functions
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).
http://www.macajournal.com/article_680048_f8dc878765ad98f0ebdf44b27b6ff0a5.pdf
2021-02-24
1
12
10.30495/maca.2021.680048
Bernoulli and Euler polynomials
Bernoulli and Euler numbers
Analytic summability
Soodeh
Mehboodi
soodehmehboodi@yahoo.com
1
Zand Institute of Higher Education, Shiraz, Iran.
AUTHOR
Mohammad
Hooshmand
hadi.hooshmand@gmail.com
2
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Generalized Ulam-Hyers stability of an alternate additive-quadratic-quartic functional equation in fuzzy Banach spaces
In this paper, we obtain and establish the generalized Ulam-Hyers stability of an additive-quadratic-quartic functional equation in fuzzy Banach spaces.
http://www.macajournal.com/article_680135_d60cd51f1af4dbd4cd12706d2b3dac94.pdf
2021-02-23
13
31
10.30495/maca.2021.680135
Additive functional equations
Quadratic functional equations
quartic functional equations
mixed type functional equations
Ulam-Hyers-Rassias stability
Fuzzy Banach space
John
Rassias
jrassias@primedu.uoa.gr
1
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
sathya24mathematics@gmail.com
2
Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai - 606 603, TamilNadu, India.
AUTHOR
Mohan
Arunkumar
drarun4maths@gmail.com
3
Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
AUTHOR
ORIGINAL_ARTICLE
Some results on disjointness preserving Fredholm operators between certain Banach function algebras
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.
http://www.macajournal.com/article_681367_92f3f2b3a35ecdaec6c83cde90844811.pdf
2021-04-29
32
39
10.30495/maca.2021.1924698.1002
Disjointness preserving
Weighted composition
Fredholm
Lida
Mousavi
mousavi.lida@gmail.com
1
Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
Sedigheh
Hosseini
s.hosseini@iauksh.ac.ir
2
Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
AUTHOR
ORIGINAL_ARTICLE
Weakly principally quasi-Baer rings and generalized triangular matrix rings
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.
http://www.macajournal.com/article_681125_83625f3e4916f6dc8ea18a5541568207.pdf
2021-02-01
39
45
10.30495/maca.2021.1925653.1004
Generalized triangular matrix ring
Annihilator
Quasi-Baer
Weakly principally quasi-Baer
Semicentral idempotent
Kamal
Paykan
k.paykan@gmail.com
1
Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
A proof of the Cauchy--Schwarz inequality from the change of reference frame
Inspired by [1] a proof of the Cauchy--Schwarz inequality is given by considering the transformation between two different inertial reference frames.
http://www.macajournal.com/article_681376_563a8d584d85c8965f309710199bea4e.pdf
2021-03-01
46
47
10.30495/maca.2021.1927475.1005
Cauchy--Schwarz inequality
reference frame
Nicola
Fabiano
nicola.fabiano@gmail.com
1
Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12--14, 11351 Belgrade, Serbia
LEAD_AUTHOR
ORIGINAL_ARTICLE
Stability of quartic functional equation in paranormed spaces
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.
http://www.macajournal.com/article_680651_4b4d55ea22b5b3dc10901cdc23cdf79b.pdf
2021-02-01
48
58
10.30495/maca.2021.1924046.1001
paranormed space
quartic functional equation
Ulam-Hyers stability
fixed point method
Karthikeyan
Subramani
karthik.sma204@yahoo.com
1
Department of Mathematics
R.M.K. Engineering College
Kavarapettai
LEAD_AUTHOR
Choonkil
Park
baak@hanyang.ac.kr
2
Department of Mathematics, Hanyang University, Republic of Korea
AUTHOR
John
Rassias
jrassias@primedu.uoa.gr
3
Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str. Aghia Paraskevi, Athens 15342, Greece.
AUTHOR