172 Results Found

This paper develops the theory of strongly continuous semigroups and abstract evolution equations in modular function spaces. We study the autonomous problem $\dot{u}\left(t\right)=Bu\left(t\right)$ with initial condition $u\left(0\right)=u_0\in L_{\rho }$, where B is the infinitesimal ge...

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched $\rho$-contractions and enriched $\rho$-Kannan...

We establish a modular-space framework for the study of tripled fixed points and tripled best proximity points. Under suitable assumptions on the underlying modular (convexity, the ${\Delta }_2$ property, uniform continuity, and uniform convexity-type pro...

In this work, we investigate the refined stability of the additive, quartic, and quintic functional equations in modular spaces with and without the ${\Delta }_2$-condition using the direct method (Hyers method). We also examine Ulam stability in 2-Banach...

In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without ${\Delta }_2$ -conditions. We study the same problem in fuzzy Banach spaces and $\beta$ -ho...

Using the direct method, we prove the Ulam stability results for the general linear functional equation of the form ${\sum }_{i=1}^m{A}_i(f\left({\phi }_i\left(\overline{x}\right))\right)=D\left(\overline{x}\right)$ for all $\overline{x}\in X^n$, where f is the unknown mapping from a linear space X over a field $\mathbb{K}\&$...

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed poi...

The current study attempts to identify a new generalized metric space structure, referred to as partial modular $b-$metric, that extends both partial modular metric space via $b-$metric space and explains the topological aspects of the new sp...

In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation $\mathfrak{R}$, we develop the framework of $\mathfrak{R}$-modular b-metric-like spaces. We establ...

We investigate the existence of solutions for the Fredholm integral equation $\mathsf{\Phi }\left(\vartheta \right)=\mathcal{G}(\vartheta ,\mathsf{\Phi }\left(\vartheta \right))+{\int }_0^1\mathcal{F}(\vartheta ,\zeta ,\mathsf{\Phi }\left(\zeta \right))d\zeta ,$ for $\vartheta \in [0,1]$, in the setting of the modular function spaces...

This study concerns Riemannian manifolds with two types of tangent vectors. Let it be given that there are two subspaces of a tangent space with the property that each tangent vector has a unique decomposition as the sum of a vector in one subspace a...

This study looks closely into the analysis of the variation of constants formula given by $\Phi \left(t\right)=S\left(t\right)\Phi \left(0\right)+{\int }_0^{t}S(t-\sigma )\mathcal{F}(\sigma ,\Phi \left(\sigma \right))d\sigma ,$ for $t\in [0,T],T>0$, within the context of modular function spaces $L_{\rho }$....

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently...

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate the stability results by using the Hyers method in modular space for quartic functional equations without using the...

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-tri...

We prove the modular convexity of the mixed norm $L^p\left({\ell }^2\right)$ on the Sobolev space $W^{1,p}\left(\mathrm{\Omega }\right)$ in a domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$ under the sole assumption that the exponent $p\left(x\right)$ is bounded away from 1, i.e., we include the case $\underset{x\in \mathrm{\Omega }}{\sup }p\left(x\right)=\&infi$...

We present the concept of multivalued mappings in generalized modular metric spaces (GMMS). In addition, we give Caristi and Feng-Liu fixed point results for this type of mappings in GMMS. Then, we obtain an application for final outcomes in the sens...

We consider a Dirichlet problem driven by the anisotropic $(p,q)$ Laplacian. In the reaction, we have a parametric partially concave term plus a “superlinear” perturbation (convex term) which need not satisfy the Ambrosetti–Rabinowitz...

This study explores how the logic of product modularity could be useful for the design of complete residential building areas. Previous research has noted that product modularity is usually only applicable if a ‘full modularization’ approach is pursu...

The objective of this paper is to rigorously define the Kadec-Klee property for modular spaces endowed with a sequential convergence structure, and to demonstrate that this property leads to normal structure in such spaces. Consequently, we establish...

This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that sati...

This article introduces a new type of $C^{*}$-algebra valued modular G-metric spaces that is more general than both $C^{*}$-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed p...

The concept of statistically deferred-weighted summability was recently studied by Srivastava et al. (Math. Methods Appl. Sci. 41 (2018), 671–683). The present work is concerned with the deferred-weighted summability mean in various aspects def...

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of cl...

In recent studies, Bibiloni-Femenias, Miñana, and Valero characterized the functions that aggregate a family of (quasi-)(pseudo)metric modulars defined over a fixed set X into a single one. In this paper, we adopt a related but different appro...

This study presents two novel frameworks, termed a quasi-modular b-metric space and a non-Archimedean quasi-modular b-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously prov...

Space robots have been playing an important role in space on-orbit operation missions. However, the traditional configuration of space robots only has a single function and cannot meet the requirements of different space missions, and the launch cost...

This paper introduces two new contractive conditions in the setting of non-Archimedean modular spaces, via a C-class function, an altering distance function, and a control function. A non-Archimedean metric modular is shaped as a parameterized family...

The research object is the installation process of modular green roofs with planters placed on the concrete roof’s surface. These roofs effectively reduce rainfall disposal, prolong the lifespan of the roof coating, and enhance urban aesthetic...

This study explores the application of modular design in the regeneration of community public spaces within rapidly transforming urban environments, using Haikou as a case study. The objective is to improve spatial quality and community sustainabilit...

This paper proposes an inner–outer loop computational framework to address the morphology optimization and pursuit–evasion control problem for space modular robots. First, a morphological design space considering the functional characteri...

We consider the problem of showing that 1 is an eigenvalue for a family of generalised transfer operators of the Farey map. This is an important problem in the thermodynamic formalism approach to dynamical systems, which in this particular case is re...

Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture the generating functions of the number of microstates of BPS black holes appearing in comp...

Vulnerable open-source component reuse can lead to security problems. At present, open-source component detection for binary programs can only reveal whether open-source components with vulnerabilities are reused, which cannot determine the specific...

Hypergroups represent a generalization of groups, introduced by Marty, that are rich in applications in several sectors of mathematics and in other fields. An important class of hypergroups called join spaces is presented in this paper, along with so...

Research on modular robots for space exploration has primarily focused on reconfiguration, with limited attention given to the maneuverability in space environment, which is essential for harnessing the advantages of reconfiguration. In this paper, a...

We introduce Brain-Inspired Modular Training (BIMT), a method for making neural networks more modular and interpretable. Inspired by brains, BIMT embeds neurons in a geometric space and augments the loss function with a cost proportional to the lengt...

This study introduces an automated method for constructing residential functional modules from the perspective of user behavior. By integrating the design structure matrix (DSM) and Fuzzy C-Means Clustering Algorithm (FCM), this approach systematical...

With the evolution of social structure and the intensification of population aging, traditional community service centers struggle to meet residents’ complex needs due to their functional singularity and spatial rigidity. In response to the con...

Within the framework of Space@Sea project, an articulated modular floating structure was developed to serve as building blocks for artificial islands. The modularity was one of the key elements, intended to provide the desired flexibility of addition...

As one of the key ways to realize the industrialization and green development of construction, prefabricated construction is conducive to saving resources and energy and improving labor productivity and quality. Aiming to solve the problem of the lac...

Functional connectivity analysis aims at assessing the strength of functional coupling between the signal responses in distinct brain areas. Usually, functional magnetic resonance imaging (fMRI) time series connections are estimated through zero-lag...

Growing urbanization, housing affordability pressures, and increasing sustainability demands have positioned modular and flexible design strategies as central approaches in contemporary residential architecture. Modularity enhances construction effic...

Modular housing represents an opportunity for the mass provision of housing of an appropriate standard, implemented sustainably. We analyzed the theoretical basis of this type of housing for refugee populations. We identified several generations of h...

This study proposes a scenario-based conceptual model for transforming underground parking structures into sustainable interior green spaces, directly addressing two core research dimensions: energy efficiency and user experience. The originality of...

An involution refers to a function that acts as its own inverse. In this paper, our focus lies on exploring two-dimensional involutive maps defined by rational functions. These functions have denominators represented by polynomials of degree one and...

To address the inability of existing space grasping mechanisms to adapt to the varying shapes and sizes of space objects, we propose a novel three-fingered space robotic hand composed of an actuated palm and deployable fingers with the aim of success...

In this paper, we find the solution of the following quadratic functional equation $n{\sum }_{1\le i<j\le n}Q\left(x_i,-,x_j\right)={\sum }_{i=1}^{n}Q\left({\sum }_{j\ne i},x_j,-,(n-1),x_i\right)$, which is derived from the gravity of the n distinct vectors $x_1,\cdots ,x_n$ in an inner product space, and prove that the stability re...

In modern robotics, actuator performance is fundamental to achieving efficient and durable motion, with compactness and torque density being especially critical. Compact actuators enable integration in space-constrained systems without compromising f...

With the increasing number of space research projects, systems that can be flexibly adapted to the respective orbital and planetary mission requirements and modified retrospectively as needed are becoming increasingly interesting. One application for...