2021
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Analytic differenceability of functions
http://www.macajournal.com/article_680048.html
10.30495/maca.2021.680048
1
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).
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1
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Soodeh
Mehboodi
Zand Institute of Higher Education, Shiraz, Iran.
Iran
soodehmehboodi@yahoo.com


Mohammad
Hooshmand
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Iran
hadi.hooshmand@gmail.com
Bernoulli and Euler polynomials
Bernoulli and Euler numbers
Analytic summability
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Generalized UlamHyers stability of an alternate additivequadraticquartic functional equation in fuzzy Banach spaces
http://www.macajournal.com/article_680135.html
10.30495/maca.2021.680135
1
In this paper, we obtain and establish the generalized UlamHyers stability of an additivequadraticquartic functional equation in fuzzy Banach spaces.
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13
31


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.
Greece
jrassias@primedu.uoa.gr


Elumalai
Sathya
Department of Mathematics, Shanmuga Industries Arts and Science College,
Tiruvannamalai  606 603, TamilNadu, India.
India
sathya24mathematics@gmail.com


Mohan
Arunkumar
Department of Mathematics, Government Arts College,
Tiruvannamalai  606 603, TamilNadu, India.
India
drarun4maths@gmail.com
Additive functional equations
Quadratic functional equations
quartic functional equations
mixed type functional equations
UlamHyersRassias stability
Fuzzy Banach space
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Some results on disjointness preserving Fredholm operators between certain Banach function algebras
http://www.macajournal.com/article_681367.html
10.30495/maca.2021.1924698.1002
1
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.
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Lida
Mousavi
Department of Mathematics, YadegareImam Khomeini (RAH) ShahreRey Branch, Islamic Azad University, Tehran, Iran
Iran
mousavi.lida@gmail.com


Sedigheh
Hosseini
Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
Iran
s.hosseini@iauksh.ac.ir
Disjointness preserving
Weighted composition
Fredholm
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Weakly principally quasiBaer rings and generalized triangular matrix rings
http://www.macajournal.com/article_681125.html
10.30495/maca.2021.1925653.1004
1
A ring $R$ is called weakly principally quasiBaer 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.
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Kamal
Paykan
Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran
Iran
k.paykan@gmail.com
Generalized triangular matrix ring
Annihilator
QuasiBaer
Weakly principally quasiBaer
Semicentral idempotent
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A proof of the CauchySchwarz inequality from the change of reference frame
http://www.macajournal.com/article_681376.html
10.30495/maca.2021.1927475.1005
1
Inspired by [1] a proof of the CauchySchwarz inequality is given by considering the transformation between two different inertial reference frames.
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Nicola
Fabiano
Vinča Institute of Nuclear Sciences  National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića
Alasa 1214, 11351 Belgrade, Serbia
Serbia
nicola.fabiano@gmail.com
CauchySchwarz inequality
reference frame
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Stability of quartic functional equation in paranormed spaces
http://www.macajournal.com/article_680651.html
10.30495/maca.2021.1924046.1001
1
In this paper, we prove the UlamHyers stability of the following quartic functional equation in paranormed spaces using both direct and fixed point methods.
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48
58


Karthikeyan
Subramani
Department of Mathematics
R.M.K. Engineering College
Kavarapettai
India
karthik.sma204@yahoo.com


Choonkil
Park
Department of Mathematics, Hanyang University, Republic of Korea
Korea, Republic Of
baak@hanyang.ac.kr


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.
Greece
jrassias@primedu.uoa.gr
paranormed space
quartic functional equation
UlamHyers stability
fixed point method