Related Experiment Video
Updated: Jan 28, 2026
12:39
A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
Published on: December 10, 2012
11.7K
A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive
Shih-Sen Chang1, Jen-Chih Yao1, Ching-Feng Wen2,3
11Center for General Education, China Medical University, Taichung, Taiwan.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study introduces a new algorithm to find common solutions for monotone inclusion and fixed point problems in Hadamard spaces. The proposed method demonstrates strong convergence, enhancing existing mathematical techniques.
Area of Science:
- Optimization Theory
- Nonlinear Analysis
- Metric Geometry
Background:
- Hadamard spaces are complete geodesic metric spaces with non-positive sectional curvature.
- Monotone inclusion problems and fixed point problems are fundamental in nonlinear analysis.
- Asymptotically nonexpansive mappings generalize nonexpansive mappings.
Purpose of the Study:
- To propose a modified viscosity implicit-type proximal point algorithm.
- To approximate a common solution for a monotone inclusion problem and a fixed point problem.
- To analyze the convergence properties of the algorithm in Hadamard spaces.
Main Methods:
- Development of a modified viscosity implicit-type proximal point algorithm.
- Application of techniques from convex analysis and fixed point theory.
- Proof of strong convergence theorems under specific conditions.
Main Results:
- The proposed algorithm successfully approximates a common solution.
- Strong convergence theorems are established for the algorithm.
- The results extend and complement existing literature on iterative algorithms.
Conclusions:
- The modified algorithm is effective for solving combined inclusion and fixed point problems.
- The convergence analysis provides theoretical guarantees for the algorithm's performance.
- This work contributes to the advancement of iterative methods in geometric analysis.
Related Concept Videos
01:27Slant Asymptotes
111
A function's behavior is often guided by asymptotic constraints, where one term dominates another, defining a limiting trend. In the given scenario, the mathematical pattern follows a rational function: a cubic term in the numerator is divided by a squared term in the denominator. This results in a function with distinct characteristics, including an oblique asymptote, critical points, and undefined regions.The function's validity is determined by the denominator, which must be nonzero. This...
111
01:17Viscosity
7.3K
When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
The SI unit of viscosity is...
The SI unit of viscosity is...
7.3K
02:57Surface Tension, Capillary Action, and Viscosity
33.2K
Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
33.2K
01:24Implicit Memories
450
Implicit memories, also known as non-declarative memories, are long-term memories that function outside of conscious awareness. These memories influence behavior and skills without explicit knowledge. This type of memory is evident in tasks like playing tennis, snowboarding, and texting. Implicit memory has three subsystems: procedural memory, conditioning, and priming. This type of memory is essential in various activities, from everyday tasks to specialized skills.
One key aspect of implicit...
One key aspect of implicit...
450
01:25Implicit Differentiation
49
In classical mechanics, motion is often described through relationships between spatial coordinates and time. A car moving along a straight highway with constant acceleration serves as a simple case where velocity is an explicit function of time. This scenario results in a linear equation, enabling straightforward analysis using basic differentiation techniques.In contrast, a satellite in circular orbit follows a path defined by an implicit function. The position of the satellite is constrained...
49
01:19Viscosity of Fluid
1.2K
Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
1.2K