Best simultaneous approximation in $L^{p}(S,X)$
Mohammad
Anvar
Department of Mathematics, Ayatollah Borujerdi University, Boroujerd, Iran
author
Mohammad
Haddadi
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
author
text
article
2022
eng
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 $1\leq p\leq\infty$.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
4
v.
1
no.
2022
1
7
http://www.macajournal.com/article_686167_c4810b95b07be02773fec41b488ed601.pdf
dx.doi.org/10.30495/maca.2021.1935786.1019
Perturbed second-order state-dependent Moreau's sweeping process
Doria
Affane
LMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria
author
Mustapha Fateh
Yarou
LMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria
author
text
article
2022
eng
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.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
4
v.
1
no.
2022
9
23
http://www.macajournal.com/article_686556_1c473036a96517f088b76f7faf903c5e.pdf
dx.doi.org/10.30495/maca.2021.1938811.1029
On the zeros and critical points of a polynomial
Mohammad
Mir
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
author
Irfan
Wani
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
author
Ishfaq
Nazir
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
author
text
article
2022
eng
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.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
4
v.
1
no.
2022
25
28
http://www.macajournal.com/article_686557_580a51528933c5f12a9f2b13c74a0b56.pdf
dx.doi.org/10.30495/maca.2021.1938758.1028
Bicomplex valued bipolar metric spaces and fixed point theorems
Siva
Gurusamy
Department of Mathematics, Alagappa University, Karaikudi-630 003, India
author
text
article
2022
eng
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.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
4
v.
1
no.
2022
29
43
http://www.macajournal.com/article_686868_2589be43eacc559fce73cdf00cdd1e4f.pdf
dx.doi.org/10.30495/maca.2021.1944542.1037
Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems
Soumeyeh
Khaleghizadeh
Departmant of Mathematics,Payame Noor University,Tehran,Iran
author
text
article
2022
eng
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.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
4
v.
1
no.
2022
45
51
http://www.macajournal.com/article_686869_abb5cf84e8785ee3ad4c1badce7c1111.pdf
dx.doi.org/10.30495/maca.2021.1944809.1038
Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces
Ljiljana
Paunovic
Teacher Education Faculty
University in Pristina-Kosovska Mitrovica
Nemanjina bb, 38218 Leposavic, Serbia
author
Parveen
Kumar
Department of Mathematics, Deenbandhu Chhotu Ram University of Science
and Technology, Murthal, Sonipat 131039, Haryana, India.
author
Savita
Malik
Department of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, India
author
Manoj
Kumar
Department of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, India
author
text
article
2022
eng
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.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
4
v.
1
no.
2022
53
70
http://www.macajournal.com/article_686870_2e10cfc70d7fc25fb1e1f304bfa0aeb9.pdf
dx.doi.org/10.30495/maca.2021.1944432.1036