Mathematical Analysis and its Contemporary Applications
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Mathematical Analysis and its Contemporary Applicationsendaily1Sat, 01 Jan 2022 00:00:00 +0330Sat, 01 Jan 2022 00:00:00 +0330Best simultaneous approximation in $L^{p}(S,X)$
http://www.macajournal.com/article_686167.html
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 $1\leq p\leq\infty$.Perturbed second-order state-dependent Moreau's sweeping process
http://www.macajournal.com/article_686556.html
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.On the zeros and critical points of a polynomial
http://www.macajournal.com/article_686557.html
Let $P(z)=a_0 + a_1z + \dots &nbsp;+ a_{n-1}z^{n-1}+z^n$ be a polynomial of degree $n.$ &nbsp;The Gauss-Lucas Theorem asserts that the zeros of the derivative $P^\prime (z)= a_1 + \dots &nbsp;+(n-1) a_{n-1}z^{n-2}+nz^{n-1},$ &nbsp;lie in the convex hull of the zeros of &nbsp; $P(z).$ Given a zero of &nbsp;$P(z)$ or $P^\prime (z),$ &nbsp;A. Aziz [1], determined regions which contain at least one zero of &nbsp;$P(z)$ 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.Bicomplex valued bipolar metric spaces and fixed point theorems
http://www.macajournal.com/article_686868.html
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.Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems
http://www.macajournal.com/article_686869.html
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.Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces
http://www.macajournal.com/article_686870.html
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.t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras
http://www.macajournal.com/article_686982.html
In this paper, we use the notion of t-norms to introduce fuzzy subalgebras, fuzzy ideals, fuzzy implicative ideals, fuzzy positive implicative ideals in BCK-algebras. Next, we clarify the links between them and investigate their properties. Finally, we consider them under intersection, cartesian product and homomorphisms(image and pre image) and we study related properties.Automatic continuity of almost Jordan derivations on special Jordan Banach algebras
http://www.macajournal.com/article_688406.html
The following is the question form of Kaplansky conjecture of 1958. Is every derivation on semisimple Banach algebra continuous? Kaplansky conjecture was proved by Johnson and Sinclair in 1968. The concept of almost Jordan derivations on Jordan Banach algebras is introduced in this article. Also, Kaplansky conjecture is extended to Jordan Banach algebras as an open question: Is every almost Jordan derivations on semisimple Jordan Banach algebras continuous?. Moreover, a partial answer to this open question is derived in the sense that every almost Jordan derivation $T$ on semisimple special Jordan Banach algebras $\Omega^{+}$, with an additional condition on $\Omega^{+}$, is continuous.