Mathematical Analysis and its Contemporary Applications
http://www.macajournal.com/
Mathematical Analysis and its Contemporary Applicationsendaily1Wed, 01 Sep 2021 00:00:00 +0430Wed, 01 Sep 2021 00:00:00 +0430On various types of compatible Jungck--Rhoades pairs of mappings in C*-algebra valued metric spaces
http://www.macajournal.com/article_683278.html
In this paper, among other things, we have&nbsp;established four different types of compatible mappings that work&nbsp;in the context of C*-algebra valued metric spaces. The&nbsp;obtained types of mappings generalize from previously known ones&nbsp;within ordinary metric spaces. We have shown by examples that these types&nbsp;of mappings are really different. They can be used to consider new fixed point results which were done in the paper for the case of common fixed points of some mappings. The results in this paper&nbsp;generalize, extend, unify, enrich and complement many known&nbsp;results in the existing literature.A new version of the Hahn Banach theorem in b-Banach spaces
http://www.macajournal.com/article_683277.html
In this paper, we introduce the notion of b-Banach spaces and we present some examples. Also, we give an important extension of the Hahn-Banach theorem in a $b$-Banach space with an application.On Palais method in b-metric like spaces
http://www.macajournal.com/article_683581.html
This paper aims to prove that the Lipschitz constant in the Banach contraction principle belongs to the whole interval [0, 1) for all the six classes of spaces viz. metric spaces, b-metric spaces, partial metric spaces, partial b-metric spaces, metric like space, and finally for more general spaces called b-metric like spaces. For the proof, the idea of Palais is used and applied in a more general setting. However, the current approach is a bit more general, because the present result is applied to spaces, where the condition d(x, y) = 0 yields x = y but not conversely. Accordingly, the outcome of the paper sums up, complements and binds together known results available in the current research literature.On quasi hemi-slant submanifolds of LP-cosymplectic manifolds
http://www.macajournal.com/article_684536.html
In this paper, we define and study quasi Hemi-slant submanifolds of Lorentzian almost contact metric manifolds. We mainly concern with quasi Hemi-slant submanifolds of LP-cosymplectic manifolds. First, we find conditions for integrability of distributions involved in the definition of quasi hemislant submanifolds of LP-cosymplectic manifolds. Further, we investigate the necessary and sufficient conditions for quasi Hemi-slant submanifolds of LP-cosymplectic&nbsp;manifolds to be totally geodesic and geometry of foliations are determined.Some approximations for an equation in modular spaces
http://www.macajournal.com/article_684537.html
In this paper, we introduce and obtain the general solution of a new mixed type quadratic-cubic functional equation. We investigate the stability of such functional equations in the modular space $X_\rho$ by applying $\Delta_2$-condition and the Fatou property (in some results) in the modular function $\rho$.Controlled g-frames in Hilbert C*-modules
http://www.macajournal.com/article_684929.html
The controlled frame was introduced in 2010 by Balazs et al. [2], with the aim to improve the efficiency of the iterative algorithms constructed for inverting the frame operator. In this paper, the concept of controlled g-frames is introduced in Hilbert C*-modules. The equivalent condition for a controlled g-frame is established using the operator theoretic approach. Some characterizations of controlled g-frames and controlled g-Bessel sequences are found out. Moreover, the relationship between g-frames and controlled g-frames are established. In the end, some perturbation results on controlled g-frames are proved.An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method
http://www.macajournal.com/article_685401.html
This study concerns the existence of positive solution for the following nonlinear boundary value problem\begin{gather*}-\Delta_{p(x)} u= a(x)h(u) + f(v) \quad\text{in }\Omega\\-\Delta_{q(x)} v=b(x)k(v) + g(u) \quad\text{in }\Omega\\u=v= 0 \quad\text{on } \partial \Omega\end{gather*}where $p(x),q(x) \in C^1(\mathbb{R}^N)$ are radial symmetric functions such that $\sup|\nabla p(x)| &lt; \infty,$ $\sup|\nabla q(x)|&lt;\infty$ and $1 &lt; \inf p(x) \leq \sup p(x) &lt;\infty,1 &lt; \inf q(x) \leq \sup q(x) &lt; \infty$, and where $-\Delta_{p(x)} u = -\mathop{\rm div}|\nabla u|^{p(x)-2}\nabla u,-\Delta_{q(x)} v =-\mathop{\rm div}|\nabla v|^{q(x)-2}\nabla v$ respectively are called $p(x)$-Laplacian and $q(x)$-Laplacian, $\Omega = B(0 , R) = \{x | |x| &lt; R\}$ is a bounded radial symmetric domain, where $R &gt; 0$ is a sufficiently large constant. We discuss the existence of positive solution via sub-supersolutions without assuming sign conditions on $f(0)$ and $g(0)$.On closedness of convolution of two sets
http://www.macajournal.com/article_685578.html
In this note, we give an abstract version of the fact that convolution of two closed and compact subsets of a hypergroup is a closed set.On a nonlinear abstract second-order integrodifferential equation part I
http://www.macajournal.com/article_685579.html
The object of this paper is to study the existence, uniqueness and continuation of the solutions of nonlinear second-order integrodifferential equations. In the&nbsp;theory of infinitesimal generator of $C_0$- semigroup in a Banach space, the fixed point theorems of Schauder and Banach are used to establish our main results.Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials
http://www.macajournal.com/article_685644.html
In this paper, an efficient numerical method based on operational matrices of the second kind Chebyshev polynomials is used for the solution of a coupled system of fractional-order integrodifferential equations that the fractional derivative isgiven in Caputo's sense. The operational matrices of the second kind Chebyshev polynomials reduce the given equations to a system of linear algebraic equations. An approximate solution is calculated by extending the functions in terms of the second kind Chebyshev polynomials and applying operational matrices. Unknown coefficients are obtained by solving the final system of linear equations. Also, convergence analysis and error bound of the solution are studied in this paper.Moreover, to check the reliability and accuracy of the given method. The numerical examples have been shown and the results of the described method are compared with the Haar wavelet method. The obtained results authenticate that the displayed method is effortless to analyze and perform such types of problems. All methods for the proposed method are applied in MATLAB (R2020b) software.Bifuzzy d-algebras under norms
http://www.macajournal.com/article_685803.html
In this paper, by using norms (t-norms and t-conorms), we introduce the notions of bifuzzy d-algebras and bifuzzy d-ideals of d-algebras and investigate several interesting properties. Next, we consider their intersection and product. Finally, we obtain some results about them under d-algebra homomorphisms.