Optimal approximate solution of minimization problems for generalized multivalued (α, L)-weak contraction mappings

2015 ◽  
Author(s):  
Chayut Kongban ◽  
Poom Kumam
Keyword(s):  
Approximate Solution ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Minimization Problems

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Approximate Solution ◽  
Best Proximity Point ◽  
Existence Theorems ◽  
Contraction Principle ◽  
Optimal Approximate Solution ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Generalized Proximal Contraction ◽  
Banach’S Contraction Principle

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which are more general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate our main results.

SOME FIXED POINT RESULTS FOR A GENERALIZED $\psi$-WEAK CONTRACTION MAPPINGS IN b-METRIC SPACES

2021 ◽  
Vol 10 (5) ◽  
pp. 2449-2468
Author(s):  
E. Bashayreh ◽  
A. Talafhah ◽  
W. Shatanawi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Contraction Mappings

In this paper, we will present the definitions and notation of generalized $\psi$-weak contraction mappings in b-metric spaces, and establish some results besides the most important properties of fixed point in orbitally complete b-metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we generalize the results of Shatanawi [7]. Some examples are given to illustrate the useability of our results.

scholarly journals Some fixed point theorems in n-normed spaces

2020 ◽  
Vol 25 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Hanan Sabah Lazam ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Basic Properties ◽  
Definition Of

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and  - (,)-Weak contraction mappings in  Banach spaces.

Optimization of Tour Line Structure Flow Assignment Model: Based on Resort Environment Pressure

2014 ◽  
Vol 926-930 ◽  
pp. 3866-3869
Author(s):  
Rong Zhao ◽  
Pei Yu Ren ◽  
Lin Chen
Keyword(s):  
Approximate Solution ◽  
Equilibrium Distribution ◽  
Ecological Environment ◽  
Distribution Model ◽  
Optimal Approximate Solution ◽  
Assignment Model ◽  
Flow Assignment ◽  
Structure Flow ◽  
Set Up ◽  
Tourist Flow

To set up a resort’s equilibrium tourist flow assignment model, the tour line features of the tourists are considered. This model firstly initiates a tourist equilibrium distribution model for the resort and then gets an optimal approximate solution when a tourist group reaches a certain scale. Next, the resort’s tourist equilibrium shunting model is built and an optimal approximate solution is provided from the present resort tourist distribution. By analyzing the results, it is found that this model is able to realize the resort’s dynamic shunting steadily, to effectively lower the resort’s congestion and to reduce the ecological environment pressure.

Endpoints of multi-valued generalized weak contraction mappings

2011 ◽  
Vol 74 (6) ◽  
pp. 2170-2174 ◽  
Author(s):  
Sirous Moradi ◽  
Farshid Khojasteh
Keyword(s):  
Weak Contraction ◽  
Contraction Mappings ◽  
Generalized Weak Contraction

scholarly journals An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Feng Yin ◽  
Guang-Xin Huang
Keyword(s):  
Approximate Solution ◽  
Iterative Algorithm ◽  
Applied Mathematics ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Optimal Approximate Solution ◽  
Numerical Examples ◽  
Reflexive Matrix ◽  
The Matrix ◽  
Residual Problem

The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min over generalized reflexive matrix . For any initial generalized reflexive matrix , by the iterative algorithm, the generalized reflexive solution can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution to a given matrix in Frobenius norm can be derived by finding the least-norm generalized reflexive solution of a new corresponding minimum Frobenius norm residual problem: with , . Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.

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