A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
4
1
2022
01
01
Best simultaneous approximation in $L^{p}(S,X)$
1
7
EN
Mohammad
Valaei
Anvar
Department of Mathematics, Ayatollah Borujerdi University, Boroujerd, Iran
mohamad.valaei@abru.ac.ir
Mohammad
R
Haddadi
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
haddadi@abru.ac.ir
10.30495/maca.2021.1935786.1019
As a counterpart to the best approximation in normed linear spaces, the best simultaneous approximation was introduced. In this paper, we shall consider relation between simultaneous proximinality $W$ in $X$ and $L^p(S,W)$ in $L^p(S,X)$ for $1leq pleqinfty$. Also, we consider the relation between w-simultaneous proximinality $W$ in $X$ and $L^p(S,W)$ in $L^p(S,X)$ for $1leq pleqinfty$.
Proximinal subspace,Simultaneous proximinal subspace,Simultaneous Chebyshev subspace,Reflexive subspace,Uniformly integrable
http://www.macajournal.com/article_686167.html
http://www.macajournal.com/article_686167_c4810b95b07be02773fec41b488ed601.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
4
1
2022
01
01
Perturbed second-order state-dependent Moreau's sweeping process
9
23
EN
Doria
Affane
0000-0002-5937-6446
LMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria
affanedoria@yahoo.fr
Mustapha Fateh
Yarou
0000-0003-4083-1813
LMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria
mfyarou@yahoo.com
10.30495/maca.2021.1938811.1029
In this paper, using a discretization approach, the existence of solutions for a class of second-order differential inclusions is stated in finite dimensional setting. The right hand side of the problem is governed by the so-called nonconvex state-dependent sweeping process and contains a general perturbation with unbounded values.
differential inclusion,uniformly prox-regular sets,unbounded perturbation,absolutely continuous solution
http://www.macajournal.com/article_686556.html
http://www.macajournal.com/article_686556_1c473036a96517f088b76f7faf903c5e.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
4
1
2022
01
01
On the zeros and critical points of a polynomial
25
28
EN
Mohammad
Ibrahim
Mir
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
ibrahimmath80@gmail.com
Irfan
Ahmad
Wani
0000-0003-1036-0512
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
irfanmushtaq62@gmail.com
Ishfaq
Nazir
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
ishfaqnazir02@gmail.com
10.30495/maca.2021.1938758.1028
Let $P(z)=a_0 + a_1z + dots + a_{n-1}z^{n-1}+z^n$ be a polynomial of degree $n.$ The Gauss-Lucas Theorem asserts that the zeros of the derivative $P^prime (z)= a_1 + dots +(n-1) a_{n-1}z^{n-2}+nz^{n-1},$ lie in the convex hull of the zeros of $P(z).$ Given a zero of $P(z)$ or $P^prime (z),$ A. Aziz [1], determined regions which contain at least one zero of $P(z)$ or $P^prime (z)$ respectively. In this paper, we give simple proofs and improved version of various results proved in [1], concerning the zeros of a polynomial and its derivative.
Polynomial,Zeros,critical points,half plane,circular region
http://www.macajournal.com/article_686557.html
http://www.macajournal.com/article_686557_580a51528933c5f12a9f2b13c74a0b56.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
4
1
2022
01
01
Bicomplex valued bipolar metric spaces and fixed point theorems
29
43
EN
Siva
Gurusamy
Department of Mathematics, Alagappa University, Karaikudi-630 003, India
gsivamaths2012@gmail.com
10.30495/maca.2021.1944542.1037
The concept of bicomplex valued bipolar metric space is introduced in this article, and some properties are derived. Also, some fixed point results of contravariant maps satisfying rational inequalities are proved for bicomplex valued bipolar metric spaces.
Bipolar metric space,Bicomplex number,Complex valued metric space,fixed point
http://www.macajournal.com/article_686868.html
http://www.macajournal.com/article_686868_2589be43eacc559fce73cdf00cdd1e4f.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
4
1
2022
01
01
Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems
45
51
EN
Soumeyeh
Khaleghizadeh
Departmant of Mathematics,Payame Noor University,Tehran,Iran
skhaleghizadeh@yahoo.com
10.30495/maca.2021.1944809.1038
This paper concerns He's Homotopy Perturbation Method (HPM) which has been applied to solve some nonlinear differential equations. In HPM, at first, we construct a homotopy that satisfies an equation which is called the perturbation equation. Moreover, in this method, the solution is considered as power series in $p$. By substituting this series into an equation and equating the coefficient of the terms with identical powers of $p$, the researcher obtained a set of equations. These equations can be solved in various methods. Here Adomian decomposition method (ADM) is employed for solving equations, obtained from the homotopy perturbation method.
Homotopy Perturbation method,Nonlinear,Adomian decomposition method
http://www.macajournal.com/article_686869.html
http://www.macajournal.com/article_686869_abb5cf84e8785ee3ad4c1badce7c1111.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
4
1
2022
01
01
Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces
53
70
EN
Ljiljana
R
Paunovic
0000-0002-5449-9367
Teacher Education Faculty
University in Pristina-Kosovska Mitrovica
Nemanjina bb, 38218 Leposavic, Serbia
ljiljana.paunovic@pr.ac.rs
Parveen
Kumar
Department of Mathematics, Deenbandhu Chhotu Ram University of Science
and Technology, Murthal, Sonipat 131039, Haryana, India.
parveenyuvi@gmail.com
Savita
Malik
Department of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, India
deswal.savita@gmail.com
Manoj
Kumar
Department of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, India
manojantil18@gmail.com
10.30495/maca.2021.1944432.1036
The aim of this paper is to prove a common fixed point theorem for two pairs of $omega$-compatible and $omega$-weakly compatible maps for extending and generalizing the results of Murthy and Prasad [12] in modular metric spaces. The main result is also illustrated by an example to demonstrate the degree of validity of our hypothesis.
Common fixed point,$emptyset$-Weak Contraction,Modular Metric Spaces,$omega-$compatible map,$omega-$weakly Compatible map
http://www.macajournal.com/article_686870.html
http://www.macajournal.com/article_686870_2e10cfc70d7fc25fb1e1f304bfa0aeb9.pdf