ORIGINAL_ARTICLE
Best simultaneous approximation in $L^{p}(S,X)$
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 $1\leq p\leq\infty$. Also, we consider the relation between w-simultaneous proximinality $W$ in $X$ and $L^p(S,W)$ in $L^p(S,X)$ for $1\leq p\leq\infty$.
http://www.macajournal.com/article_686167_c4810b95b07be02773fec41b488ed601.pdf
2022-01-01
1
7
10.30495/maca.2021.1935786.1019
Proximinal subspace
Simultaneous proximinal subspace
Simultaneous Chebyshev subspace
Reflexive subspace
Uniformly integrable
Mohammad
Anvar
mohamad.valaei@abru.ac.ir
1
Department of Mathematics, Ayatollah Borujerdi University, Boroujerd, Iran
LEAD_AUTHOR
Mohammad
Haddadi
haddadi@abru.ac.ir
2
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
AUTHOR
ORIGINAL_ARTICLE
Perturbed second-order state-dependent Moreau's sweeping process
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.
http://www.macajournal.com/article_686556_1c473036a96517f088b76f7faf903c5e.pdf
2022-01-01
9
23
10.30495/maca.2021.1938811.1029
differential inclusion
uniformly prox-regular sets
unbounded perturbation
absolutely continuous solution
Doria
Affane
affanedoria@yahoo.fr
1
LMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria
AUTHOR
Mustapha Fateh
Yarou
mfyarou@yahoo.com
2
LMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria
LEAD_AUTHOR
ORIGINAL_ARTICLE
On the zeros and critical points of a polynomial
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.
http://www.macajournal.com/article_686557_580a51528933c5f12a9f2b13c74a0b56.pdf
2022-01-01
25
28
10.30495/maca.2021.1938758.1028
Polynomial
Zeros
critical points
half plane
circular region
Mohammad
Mir
ibrahimmath80@gmail.com
1
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
AUTHOR
Irfan
Wani
irfanmushtaq62@gmail.com
2
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
LEAD_AUTHOR
Ishfaq
Nazir
ishfaqnazir02@gmail.com
3
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
AUTHOR
ORIGINAL_ARTICLE
Bicomplex valued bipolar metric spaces and fixed point theorems
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.
http://www.macajournal.com/article_686868_2589be43eacc559fce73cdf00cdd1e4f.pdf
2022-01-01
29
43
10.30495/maca.2021.1944542.1037
Bipolar metric space
Bicomplex number
Complex valued metric space
fixed point
Siva
Gurusamy
gsivamaths2012@gmail.com
1
Department of Mathematics, Alagappa University, Karaikudi-630 003, India
LEAD_AUTHOR
ORIGINAL_ARTICLE
Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems
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.
http://www.macajournal.com/article_686869_abb5cf84e8785ee3ad4c1badce7c1111.pdf
2022-01-01
45
51
10.30495/maca.2021.1944809.1038
Homotopy Perturbation method
Nonlinear
Adomian decomposition method
Soumeyeh
Khaleghizadeh
skhaleghizadeh@yahoo.com
1
Departmant of Mathematics,Payame Noor University,Tehran,Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces
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.
http://www.macajournal.com/article_686870_2e10cfc70d7fc25fb1e1f304bfa0aeb9.pdf
2022-01-01
53
70
10.30495/maca.2021.1944432.1036
Common fixed point
$emptyset$-Weak Contraction
Modular Metric Spaces
$omega-$compatible map
$omega-$weakly Compatible map
Ljiljana
Paunovic
ljiljana.paunovic@pr.ac.rs
1
Teacher Education Faculty
University in Pristina-Kosovska Mitrovica
Nemanjina bb, 38218 Leposavic, Serbia
LEAD_AUTHOR
Parveen
Kumar
parveenyuvi@gmail.com
2
Department of Mathematics, Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Sonipat 131039, Haryana, India.
AUTHOR
Savita
Malik
deswal.savita@gmail.com
3
Department of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, India
AUTHOR
Manoj
Kumar
manojantil18@gmail.com
4
Department of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, India
AUTHOR