Related Experiment Video
Updated: Feb 6, 2026
06:34
Application of a Coupling Agent to Improve the Dielectric Properties of Polymer-Based Nanocomposites
Published on: September 19, 2020
6.4K
Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
Binayak S Choudhury1, Pranati Maity2, Nikhilesh Metiya3
11Department of Mathematics, Indian Institute of Engineering Science and Technology, Howrah, India.
Journal of Inequalities and Applications
|August 24, 2018
Summary
This study introduces a novel method to calculate the distance between two sets using a multivalued coupling. The research defines best proximity points to determine this distance, with applications in metric and Banach spaces.
Area of Science:
- Mathematical Analysis
- Set Theory
- Topology
Background:
- Calculating distances between sets is fundamental in various mathematical fields.
- Existing methods may have limitations in certain complex spaces.
- Multivalued mappings offer advanced tools for exploring set relationships.
Purpose of the Study:
- To develop an iterative approach for determining the distance between two sets.
- To introduce and define "best proximity points" for multivalued couplings.
- To extend these findings to specific geometric spaces like uniformly convex Banach spaces.
Main Methods:
- Utilizing a specifically defined multivalued coupling for iterative distance calculation.
- Deducing a main theorem within the framework of metric spaces.
- Applying geometric properties of uniformly convex Banach spaces for specialized results.
Main Results:
- An iterative method is established to find the distance between two sets.
- The concept of best proximity points is defined and utilized to realize this distance.
- The theoretical framework is successfully applied to uniformly convex Banach spaces.
Conclusions:
- The proposed iterative method effectively ascertains the distance between sets.
- Best proximity points provide a concrete realization of the distance.
- The study demonstrates the utility of multivalued couplings in geometric analysis.
Related Concept Videos
01:29Application of Linearization and Approximation
94
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
94
01:29Distance Problem
71
When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
71
01:24Approximate Integration
53
In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
53
01:26Linearization and Approximation
67
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
67
02:12Short-distance Transport of Resources
17.7K
Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
17.7K
01:28Accuracy, limits, and approximation
1.3K
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
1.3K