1. Best simultaneous approximation in $L^{p}(S,X)$

Mohammad Valaei Anvar; Mohammad R Haddadi

Volume 4, Issue 1 , Winter 2022, Pages 1-7


  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 ...  Read More

2. Perturbed second-order state-dependent Moreau's sweeping process

Doria Affane; Mustapha Fateh Yarou

Volume 4, Issue 1 , Winter 2022, Pages 9-23


  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 ...  Read More

3. On the zeros and critical points of a polynomial

Mohammad Ibrahim Mir; Irfan Ahmad Wani; Ishfaq Nazir

Volume 4, Issue 1 , Winter 2022, Pages 25-28


  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 ...  Read More

4. Bicomplex valued bipolar metric spaces and fixed point theorems

Siva Gurusamy

Volume 4, Issue 1 , Winter 2022, Pages 29-43


  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.  Read More

5. Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems

Soumeyeh Khaleghizadeh

Volume 4, Issue 1 , Winter 2022, Pages 45-51


  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 ...  Read More

6. Common fixed point results for ω-compatible and ω-weakly compatible maps in modular metric spaces

Ljiljana R Paunovic; Parveen Kumar; Savita Malik; Manoj Kumar

Volume 4, Issue 1 , Winter 2022, Pages 53-70


  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 ...  Read More