A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98904120220101Best simultaneous approximation in $L^{p}(S,X)$1768616710.30495/maca.2021.1935786.1019ENMohammad ValaeiAnvarDepartment of Mathematics, Ayatollah Borujerdi University, Boroujerd, IranMohammad RHaddadiDepartment of Mathematics, Ayatollah Boroujerdi University, Boroujerd, IranJournal Article20210717As 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 $1leq pleqinfty$.A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98904120220101Perturbed second-order state-dependent Moreau's sweeping process92368655610.30495/maca.2021.1938811.1029ENDoriaAffaneLMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria0000-0002-5937-6446Mustapha FatehYarouLMPA Laboratory, Department of Mathematics, Jijel University, PB98, Cite Ouled Aissa, Jijel, Algeria0000-0003-4083-1813Journal Article20210826In 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.A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98904120220101On the zeros and critical points of a polynomial252868655710.30495/maca.2021.1938758.1028ENMohammad IbrahimMirDepartment of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, IndiaIrfan AhmadWaniDepartment of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India0000-0003-1036-0512IshfaqNazirDepartment of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, IndiaJournal Article20210825Let $P(z)=a_0 + a_1z + dots + a_{n-1}z^{n-1}+z^n$ 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.A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98904120220101Bicomplex valued bipolar metric spaces and fixed point theorems294368686810.30495/maca.2021.1944542.1037ENSivaGurusamyDepartment of Mathematics, Alagappa University, Karaikudi-630 003, IndiaJournal Article20211109The 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.A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98904120220101Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems455168686910.30495/maca.2021.1944809.1038ENSoumeyehKhaleghizadehDepartmant of Mathematics,Payame Noor University,Tehran,IranJournal Article20211112This 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.A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98904120220101Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces537068687010.30495/maca.2021.1944432.1036ENLjiljana RPaunovicTeacher Education Faculty
University in Pristina-Kosovska Mitrovica
Nemanjina bb, 38218 Leposavic, Serbia0000-0002-5449-9367ParveenKumarDepartment of Mathematics, Deenbandhu Chhotu Ram University of Science
and Technology, Murthal, Sonipat 131039, Haryana, India.SavitaMalikDepartment of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, IndiaManojKumarDepartment of Mathematics, Faculty of Science, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana, IndiaJournal Article20211108The 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.