@article {
author = {Anvar, Mohammad and Haddadi, Mohammad},
title = {Best simultaneous approximation in $L^{p}(S,X)$},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {4},
number = {1},
pages = {1-7},
year = {2022},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1935786.1019},
abstract = {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 $1\leq p\leq\infty$.},
keywords = {Proximinal subspace,Simultaneous proximinal subspace,Simultaneous Chebyshev subspace,Reflexive subspace,Uniformly integrable},
url = {http://www.macajournal.com/article_686167.html},
eprint = {http://www.macajournal.com/article_686167_c4810b95b07be02773fec41b488ed601.pdf}
}
@article {
author = {Affane, Doria and Yarou, Mustapha Fateh},
title = {Perturbed second-order state-dependent Moreau's sweeping process},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {4},
number = {1},
pages = {9-23},
year = {2022},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1938811.1029},
abstract = {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.},
keywords = {differential inclusion,uniformly prox-regular sets,unbounded perturbation,absolutely continuous solution},
url = {http://www.macajournal.com/article_686556.html},
eprint = {http://www.macajournal.com/article_686556_1c473036a96517f088b76f7faf903c5e.pdf}
}
@article {
author = {Mir, Mohammad and Wani, Irfan and Nazir, Ishfaq},
title = {On the zeros and critical points of a polynomial},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {4},
number = {1},
pages = {25-28},
year = {2022},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1938758.1028},
abstract = {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.},
keywords = {Polynomial,Zeros,critical points,half plane,circular region},
url = {http://www.macajournal.com/article_686557.html},
eprint = {http://www.macajournal.com/article_686557_580a51528933c5f12a9f2b13c74a0b56.pdf}
}
@article {
author = {Gurusamy, Siva},
title = {Bicomplex valued bipolar metric spaces and fixed point theorems},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {4},
number = {1},
pages = {29-43},
year = {2022},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1944542.1037},
abstract = {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.},
keywords = {Bipolar metric space,Bicomplex number,Complex valued metric space,fixed point},
url = {http://www.macajournal.com/article_686868.html},
eprint = {http://www.macajournal.com/article_686868_2589be43eacc559fce73cdf00cdd1e4f.pdf}
}
@article {
author = {Khaleghizadeh, Soumeyeh},
title = {Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {4},
number = {1},
pages = {45-51},
year = {2022},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1944809.1038},
abstract = {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.},
keywords = {Homotopy Perturbation method,Nonlinear,Adomian decomposition method},
url = {http://www.macajournal.com/article_686869.html},
eprint = {http://www.macajournal.com/article_686869_abb5cf84e8785ee3ad4c1badce7c1111.pdf}
}
@article {
author = {Paunovic, Ljiljana and Kumar, Parveen and Malik, Savita and Kumar, Manoj},
title = {Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces},
journal = {Mathematical Analysis and its Contemporary Applications},
volume = {4},
number = {1},
pages = {53-70},
year = {2022},
publisher = {A.I.A University Publishing Group.},
issn = {2716-9890},
eissn = {2716-9898},
doi = {10.30495/maca.2021.1944432.1036},
abstract = {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.},
keywords = {Common fixed point,$emptyset$-Weak Contraction,Modular Metric Spaces,$omega-$compatible map,$omega-$weakly Compatible map},
url = {http://www.macajournal.com/article_686870.html},
eprint = {http://www.macajournal.com/article_686870_2e10cfc70d7fc25fb1e1f304bfa0aeb9.pdf}
}