Modular Spaces Research Articles

Generalized modular fractal spaces and fixed point theorems

In this article, we introduce a new concept of Hausdorff distance through generalized modular metric on nonempty compact subsets and study some topological properties of it. This concept with contraction theory and the iterated function system (IFS) helps us to define a generalized modular fractal space.

Modular Maximal Estimates of Schrödinger Equations

This paper offers the maximal estimates of the solutions of some initial value problems on modular spaces. Our results include the estimates for the solutions of Schrödinger equation.

Nadler’s Theorem on Incomplete Modular Space

This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented. Further, we prove Nadler’s Theorem and some fixed point results on orthogonal modular spaces. We present an application to a particular form of integral inclusion to support our proposed version of Nadler’s theorem.

$\mathcal{F-}$relative $\mathcal{A-}$summation process for double sequences and abstract Korovkin type theorems

In this paper, we first introduce the notions of $\mathcal{F-}$relative modular convergence and $\mathcal{F-}$relative strong convergence for double sequences of functions. Then we prove some Korovkin-type approximation theorems via $\mathcal{F-}$relative $\mathcal{A}-$summation process on modular spaces for double sequences of positive linear operators. Also, we present a non-trivial application such that our Korovkin-type approximation results in modular spaces are stronger than the classical ones and we present some estimates of rates of convergence for abstract Korovkin-type theorems. Furthermore, we relax the positivity condition of linear operators in the Korovkin theorems and study an extension to non-positive operators.

C*-algebra valued modular S-metric spaces with applications in fixed point theory

In this paper, we introduce C*-algebra valued modular S-metric spaces. Some common fixed point results for S-weak operator pair on C*-algebra valued modular S-metric spaces is given with suitable examples. Stability of the fixed point and application for a system of integral equations are also discussed here.

Common fixed point theorems for several multivalued mappings on proximinal sets in regular modular space

In this paper, we found a common fixed point for several multivalued mappings on proximinal sets in regular modular metric space. Also, we introduced the notions of conjoint F-proximinal contraction as well as conjoint F-proximinal contraction of Hardy–Rogers-type for several multivalued mappings. Furthermore, we enhanced our results by giving an application in integral equations.

Convergence Results for Total Asymptotically Nonexpansive Monotone Mappings in Modular Function Spaces

In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space.

Some fixed-point theorems for a general class of mappings in modular G-metric spaces

PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.Research limitations/implicationsAnalytical and theoretical results.Practical implicationsThe results of this paper can be applied in science and engineering.Social implicationsThe results of this paper is applicable in certain social sciences.Originality/valueThe results of this paper are new and will open up new areas of research in mathematical sciences.

Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings

This paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems for multivalued nonexpansive mappings in modular spaces.

Common fixed point of generalized weakly contractive mappings on orthogonal modular spaces with applications

In this paper, we provide certain conditions under which guarantee the existence of a common fixed point for weakly contractive mappings defined on orthogonal modular spaces. Also, Banach fixed point theorem on an orthogonal modular space without completeness is obtained. To prove much stronger and more applicable results, some strong assumptions such as the convexity and the Fatou property of a modular are relaxed.

Convexity property and fixed-point theorems in CΩ-modular space

The purpose of this study is to introduce a new concept of the modular space, which is CΩ-modular space, and then some of the convex properties are discussed. We also study finding fixed-point in CΩ-modular space.

Stability of a ramanujan type additive functional equation

In this paper, the authors achieve the generalized Ulam - Hyers stability of a Ramanujan Type Additive Functional Equation in Paranormed Spaces and Modular spaces via classical Hyers Method.

Аппроксимация затухающих колебаний крупногабаритных космических конструкций

It is possible to use data recorded by onboard acceleration sensors to verify mathematical models of large modular space structures in terms of simulating dynamic processes. The paper investigates an approach to approximating damped oscillations caused by dynamic impacts during operation. Initially, we approximate the response of the structure by summing damped harmonics derived from analysing the frequency spectrum of the dynamic process; then we use the Levenberg --- Marquardt algorithm in the parameter space of the harmonic set to find the best match between the real dynamic process and its approximation. We propose a modification of the approach considered which involves employing single harmonics to perform successive approximations of the function of time to be fitted. We show that it is possible to apply the approach proposed to identifying the frequency and dissipative parameters of the structure under consideration. The paper presents the results of testing the approach proposed via artificially generated noisy acceleration functions of time with known parameters, which were reconstructed with a sufficient degree of accuracy. A real-world example provided comprises the results of analysing the ISS accelerometer readings recorded against the background of damped vibrations in its structure that were caused by burns of its attitude control engines

Common Fixed Points of w-Compatible Maps in Modular A-metric Spaces

The aim of this paper is to prove a common fixed point theorem for two ω-compatible maps in modular A-metric spaces. The main result is also illustrated by an example to demonstrate the degree of validity of our hypothesis.

Convexity and boundedness relaxation for fixed point theorems in modular spaces

<p>Although fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. In this paper, we focus on convexity and boundedness of modulars in fixed point results taken from the literature for contractive correspondence and single-valued mappings. To relax these two assumptions, we seek to identify the ties between modular and b-metric spaces. Afterwards we present an application to a particular form of integral inclusions to support our generalized version of Nadler’s theorem in modular spaces.</p>

Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

This research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

Structure and bases of modular spaces sequences (M 2k (Γ 0 (N))) k∈ℕ *

Structure and bases of modular spaces sequences <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>M</mml:mi> <mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:mrow> </mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>Γ</mml:mi> <mml:mn>0</mml:mn> </mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow> <mml:mrow><mml:mi>k</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi>ℕ</mml:mi> <mml:mo>*</mml:mo> </mml:msup></mml:mrow> </mml:msub></mml:math>

Bi-additive s-functional inequalities and biderivation in modular spaces

Bi-additive s-functional inequalities and biderivation in modular spaces

A survey on recent results in Korovkin’s approximation theory in modular spaces

In this paper we give a survey about recent versions of Korovkin-type theorems for modular function spaces, a class which includes $L^p$, Orlicz, Musielak-Orlicz spaces and many others. We consider various kinds of modular convergence, using certain summability processes, like triangular matrix statistical convergence, and filter convergence (which are generalizations of the statistical convergence). Finally, wwe consider an abstract axiomatic convergence which includes the previous ones and even almost convergence, which is not generated by any filter, as we show by an example.

$rho$-Attractive Elements in Modular Function Spaces

In this paper, we introduce the notion of ρ-attractive elements in modular function spaces. A new class of mappings called ρ-k-nonspreading mappings is also introduced. Making a good use of the two notions, we first prove existence results and then some approximation results in the setup of modular function spaces. An example is presented to support the results proved herein.