Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Types of Errors: Detection and Minimization01:12

Types of Errors: Detection and Minimization

12.0K
Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
12.0K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.6K
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
1.6K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

2.1K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
2.1K
Systematic Error: Methodological and Sampling Errors01:15

Systematic Error: Methodological and Sampling Errors

11.3K
In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
11.3K
Random and Systematic Errors01:20

Random and Systematic Errors

16.0K
Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
16.0K
Random and Systematic Errors01:20

Random and Systematic Errors

926
926

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

In-silico combinatorial design and pharmacophore modeling of potent antimalarial 4-anilinoquinolines utilizing QSAR and computed descriptors.

SpringerPlus·2017
Same journal

Erratum to: Implication of Paris Agreement in the context of long-term climate mitigation goals.

SpringerPlus·2017
Same journal

Erratum to: Associations between adherence, depressive symptoms and health-related quality of life in young adults with cystic fibrosis.

SpringerPlus·2017
Same journal

Erratum to: Numerical method to compute acoustic scattering effect of a moving source.

SpringerPlus·2017
Same journal

Identifying appropriate protected areas for endangered fern species under climate change.

SpringerPlus·2017
Same journal

An Algorithm to detect balancing of iterated line sigraph.

SpringerPlus·2017

Related Experiment Video

Updated: Mar 22, 2026

Errors as a Means of Reducing Impulsive Food Choice
07:07

Errors as a Means of Reducing Impulsive Food Choice

Published on: June 5, 2016

9.3K

A note on "Implicit iterative process with errors".

Esra Yolacan1

  • 1Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240 Turkey.

Springerplus
|April 12, 2016
PubMed
Summary

This study introduces a new iterative process for solving problems involving nonexpansive mappings in Banach spaces. The findings demonstrate strong convergence, improving upon existing mathematical results.

Keywords:
Common fixed pointsImplicit iterative process with errorsTotal asymptotically nonexpansive mappings

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.2K
Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition
14:01

Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition

Published on: May 22, 2015

43.5K

Related Experiment Videos

Last Updated: Mar 22, 2026

Errors as a Means of Reducing Impulsive Food Choice
07:07

Errors as a Means of Reducing Impulsive Food Choice

Published on: June 5, 2016

9.3K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.2K
Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition
14:01

Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition

Published on: May 22, 2015

43.5K

Area of Science:

  • Nonlinear analysis
  • Functional analysis
  • Fixed-point theory

Background:

  • Iterative processes are crucial for approximating solutions in mathematical analysis.
  • Asymptotically nonexpansive mappings are a significant class of operators in Banach spaces.
  • Convergence theorems provide theoretical guarantees for the success of iterative methods.

Purpose of the Study:

  • To introduce a novel implicit iterative process incorporating mixed errors.
  • To analyze the convergence properties of this process for a finite family of total asymptotically nonexpansive mappings.
  • To establish strong convergence theorems in a uniformly convex Banach space.

Main Methods:

  • Development of an implicit iterative process with mixed errors.
  • Application of techniques from nonlinear analysis and fixed-point theory.
  • Rigorous mathematical proofs to establish convergence criteria.

Main Results:

  • The proposed implicit iterative process demonstrates strong convergence.
  • The convergence is established for a finite family of total asymptotically nonexpansive mappings.
  • The theoretical framework is set within uniformly convex Banach spaces.

Conclusions:

  • The introduced iterative process is effective for approximating fixed points of the specified mappings.
  • The results offer significant improvements and extensions to existing literature in the field.
  • This work contributes to the advancement of convergence theory in Banach spaces.