Modular Spaces Research Articles

Interpolative Meir–Keeler Mappings in Modular Metric Spaces

Modular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular metric spaces. In particular, we examine the existence of interpolative Meir–Keeler contraction types via admissible mappings for fixed point theory. Our results bring together several results available in the current corresponding literature.

Adaptive Ephemeral Interiority: Upcycling Site Specific Interiors

Adaptive reuse in architecture refers to the process of redesigning, converting, and reappropriating existing spaces for functions different from the ones they were originally designed for. This research is a case study showing an alternative to this concept, re-purposing aviation parts and finding new programmatic functions in the design learning studio. The pedagogy approach, adopted by a design studio in the United Arab Emirates (UAE), presents the fluidity of adaptive interiority against rigidity and site specificity. The research results in the creation of adaptive modular spaces and ephemeral interiority through upcycling design, flexibility, materiality, reusability, recyclability, and connectivity while simultaneously showcasing the rigorous interplay of innovation, research, science, and technology. The case study design studio was based at Zayed University and partnered with Etihad Airways, the national carrier of the UAE, highlighting the importance of industry and education as interdisciplinary collaborations. The paper looks at the pedagogical approach and examines the conducted process and evaluates the outcomes and shortcomings, including those inflicted by the COVID-19 world health pandemic. It argues for ‘adaptive interiority,’ inclusion in the adaptive reuse framework and a further reflection on the large vision and possible future impact within the UAE’s social and architectural context.

Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem

Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem

Spatial Adaptive Arrangement of Street Vendors to the Covid-19 Pandemic in Simpang Lima, Semarang, Indonesia

Covid-19 has caused a global crisis that has affected various aspects of life, including urban spatial arrangement, such as arrangement of street vendors activities in urban public spaces. As one of the activities supports that have developed due to primary urban activities, street vendors often occupy public spaces, as can be seen in Simpang Lima in Semarang, a central business and culinary tourism district where street vendors sell their good on pedestrian ways. Moreover, these vendors have been stabilized to accommodate their existence in sustainable manner. Hence, it is necessary to review the adaption of this arrangement to pandemics, bearing in mind the necessity of precautions against Covid-19 and physical distancing in accordance with the recommendations of the World Health Organization (WHO). This research applied quantitative methods and obtained data by collecting questionnaires and observations, showing that street vendors’ spatial arrangement within the food court concept in Simpang Lima had been adaptive to the Covid-19 pandemic reviewed from space arrangement, vending facilities, and health protocol applications. Among the precautions implemented for each vendor are the arrangement of space using modular spaces of size 3 by 3 meters, so that each has their own adaptive space, in accordance with physical distancing; maintaining spaces properly ventilated; applying a distance of more than one meter between any two tables in the consumer dining space; washing utensils in running water to maximize cleanliness; and ensuring the availability of public sinks with running water for customers and the public.

Some Properties Of Soft Modular Space

In this paper, we will present a definition of soft modular space and some properties of soft modular (convergent, continuous, bounded) are explained instead of the prevailing definition.

Fixed points of $\rho$-nonexpansive mappings using MP iterative process

This research article introduces a new iterative process called MP iteration and prove some convergence and approximation results for the fixed points of $\rho$-nonexpansive mappings in modular function spaces. To demonstrate that MP iterative process converges faster than some well-known existing iterative processes for $\rho$-nonexpansive mappings, we constructed some numerical examples. In the end, the concept of summably almost T-stability for MP iterative process is discussed.

Extrapolation on function and modular spaces, and applications

We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations.

Fixed point theorems for mappings with a contractive iterate at a point in modular metric spaces

Fixed point theorems for mappings with a contractive iterate at a point in modular metric spaces

New Trend Spaces in Contemporary Architecture

This article focuses on the production methods of contemporary style spaces, which are fundamentally different from traditional spaces, especially by exhibiting; flexibility, dynamism, and diversity themes in the formation of contemporary spatial relations as a conceptual tool. Space is naturally a unit with defined boundaries and we stand in the middle of this unit, thus, spaces have more or less boundaries, and when these boundaries become more transparent, permeable, and dynamic instead of rigid and fixed the spatial values of spaces increase and turn into flexible spaces. In this framework, spatial design is an organization that is; flexible and dynamic with various scenarios and necessities, it’s the art of space-making with both 2-d (two-dimensional) and 3-d (three-dimensional) tools and methods. Spatial design is creative and innovative, hence contemporary. By adapting spatial design; instead of traditional fixed walls, it is possible to obtain scenario-based, flexible, multi-functional spaces within an artistic value like stage-designs. In the article, first of all, the concept of spatial design has been introduced, based on a number of basic topics; the first is, the new space relations used in today’s interiors instead of the traditional corridor and cell space relation with ‘depth/density/integration’ space relations. Secondly, contemporary style new space identifiers have been introduced, instead of traditional reinforced concrete walls. Contemporary style new spatial identifiers that are presented in the paper are; I/L/U type vertical panels, point-like dividers, level differences, furniture and convexity, material & texture difference (all 3 faces walls/floors/ceilings), color change, 3d space modules (spatial furniture), and finally ceilings & lighting. 
 By this study, it’s mainly aimed to put forth the changing design principles of contemporary interiors that have developed recent years differently from the past. At this point, study brings out the research question -1 : What are the changing design parameters of today’s interiors? In addition, research question-2: What are new space definers instead of walls? As indicated by the hypothesis of the study, it is aimed to make a comparative analysis of interiors between periods, to reveal the differences and explain new methods for contemporary interiors. To demonstrate the changing design principles of interiors’ today; spatial design will be introduced with, new spatial relations, new space types, new space identifiers that creates todays; dynamic, flexible and multifunctional interiors. At this point, research question-3 appears as; ‘What is ‘expandability-flexibility- convexity’ and how each used with spatial design? Third question is very clearly shed a light to the hypothesis of the study and defines new spatial relations as; depth, density and integration. By using spatial tools, enclosed spaces that are syntax via corridor system leaves it’s place to spatial design, which creates sub-spaces with in a one big space without existing walls. At spatial design, there is no existing 4 walls, instead, sub-spaces are formed very quickly to the changing scenarios and necessary modifications easily so it’s flexible. On the other hand, spatial design, can adapt to time, with 7/24 logic, thus, some spaces can expand, get bigger time to time in order to react changing functions than shrink to it’s normal sizes after the activity. Thus, expandability tool supports flexibility by the way space adaptation. Lastly, integration tool, can be used to create modular spaces, through necessities, 1 module , 2 modules or 3 modules..etc. spaces can integrate easily by the help of light dividers and integrated spaces and activities can take place.
 As indicated above, hypothesis of the study is based on spatial design and it has 3 main research questions to define/answer the main problem. In the study, it’s aimed to demonstrate solutions for these 3 problems; 1)What are the changing design parameters of today’s interiors?, 2) What are new space definers?, 3) ‘what are ‘expandability-flexibility- convexity’ tools ?
 The methodology consists of two main parts, the first of which includes a comprehensive literature review on; space, spatiality, spatial relations and contemporary space identifiers and the definitions of;expandability, flexibility, convexity. Secondly, area analyzes have been made on the contemporary interior designs, that are determined as the hypothesis of the study. Analyzes and findings are presented within the framework of ‘contemporary period spatiality’ versus ‘traditional spatial organization’ as a comparative design investigation. As a result, the aim of this study is; the introduction and presentation of spatial design as a method of contemporary space production techniques.

Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods

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 Fatou property, without using the Δb-condition and without using both the Δb-condition and the Fatou property. Moreover, we investigate the stability results for this functional equation with the help of a fixed-point technique involving the idea of the Fatou property in modular spaces. Furthermore, a suitable counter example is also demonstrated to prove the non-stability of a singular case.

Thermal-Structural Analysis of the Support Structure for a Modular Space Deployable Antenna

A modular space deployable antenna has the advantages of extensibility, adaptability, and versatility, which is an ideal structure to meet the development trend of large aperture, high precision, and light weight for the deployable antenna in the future. To date, there are few reports on the temperature response of a modular deployable antenna in the thermal alternating environment in orbit. The aim of this study is at investigating the influence of a modular deployable antenna support structure on the surface accuracy and stability under the space thermal alternating environment. For this purpose, the thermal-structure analysis of the deployable antenna support structure was carried out by ANSYS APDL finite-element software. Using the transient temperature field obtained by thermal analysis as the boundary condition, the coupling law of stress development and thermal deformation of the support chord and cable caused by the antenna structure constraint position and other parameters is analyzed. In a uniform thermal field, the thermal stress of cables in the central module of the structure is the highest and that of the chord components in the same-circle modules is essentially the same. The thermally stress of the upper chords increases progressively toward the outer module, whereas that of cables decreases in the same direction. The thermal deformation at the upper-layer centroid of the structure can reach about 15 mm, so the influence on the accuracy of the antenna cannot be ignored. When the splicing vertical rod of adjacent modules in the outermost of the support structure is taken as the constraint connecting with the extension arm, the thermal deformation of the structure is minimum. The heat-insulating composite coating should be adopted on the surface of the antenna structure to reduce the thermal deformation and improve the adaptability. The thermal-structural analysis model proposed in this study could accurately estimate the behaviour of thermal deformation for the modular space deployable antenna, but the further coupling condition of the nonuniform temperature field could still be conducted. The results can provide a reference for the basic theory and engineering application of thermal-structural analysis for extralarge-aperture modular deployable antennas in the future.

Relation between electrical resistance and conductance using multifarious functional equations and applications to parallel circuit

In this paper, we introduce a new generalized p-dimensional multifarious radical reciprocal functional equation combining three classical means: arithmetic, geometric, and harmonic. Mainly, we find its general solution and stability related to the Ulam problem in modular spaces by using the fixed point method with suitable counterexamples. Importantly, in this paper, we illustrate the geometrical interpretation and applications of the introduced Pythagorean means multifarious functional equation in connection with the parallel circuit. Furthermore, we provide a formula for finding the equivalent resistance R_{mathrm{eq}} of parallel electrical circuit using functional equations, which relates the electrical resistances and conductances with suitable examples.

Solution and Stability of Quartic Functional Equations in Modular Spaces by Using Fatou Property

We propose a novel generalized quartic functional equation and investigate its Hyers–Ulam stability in modular spaces using a fixed point technique and the Fatou property in this paper.

A common fixed point theorem for new type compatible maps on modular metric spaces

In this paper, we discuss a new definition of [Formula: see text]-compatible maps in a modular metric space, prove a common fixed point theorem and utilize them to get a solution of a Volterra type integral equation.

Fixed point results of $$\beta _Y$$-Geraghty type contractive mapping in modular metric-like spaces

Fixed point results of $$\beta _Y$$-Geraghty type contractive mapping in modular metric-like spaces

On fixed point theorems for a class of $$\alpha$$-$${\hat{v}}$$-Meir–Keeler-type contraction mapping in modular extended b-metric spaces

On fixed point theorems for a class of $$\alpha$$-$${\hat{v}}$$-Meir–Keeler-type contraction mapping in modular extended b-metric spaces

SOME COINCIDENCE POINT THEOREMS IN MODULAR SPACES

In metric spaces, there are quasi-contraction mappings and Suzuki-contraction mapping, that are generalization of contraction mappings. In this article, we give coincidence point theorems of quasi-contraction mappings and Suzuki-contraction mappings in modular spaces, that are generalizations of fixed point theorem of quasi-contractraction mappings and Suzuki-contraction theorem in modular spaces.

Common fixed point theorems in modular metric spaces with applications to nonlinear integral equation of Urysohn type

Common fixed point theorems in modular metric spaces with applications to nonlinear integral equation of Urysohn type

Fixed Point Results on Partial Modular Metric Space

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-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed.

A study of some new multivalued fixed point results in a modular like metric space with graph

A study of some new multivalued fixed point results in a modular like metric space with graph