scholarly journals A Stackelberg-population competition model via variational inequalities and fixed points

2020 ◽  
Vol 36 (2) ◽  
pp. 331-339
Author(s):  
YUE-TIAN ZHAN ◽  
◽  
XUE-SONG LI ◽  
NAN-JING HUANG ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Competition Model ◽  
Stackelberg Competition ◽  
Mild Conditions ◽  
Population Games ◽  
Equilibrium Response ◽  
Response Set ◽  
Inequality Technique ◽  
Population Competition ◽  
Population Equilibrium

In this paper, we introduce and study a new Stackelberg-population competition model which captures the desired features of both population games and Stackelberg competition model within the same framework. We obtain some characterization results for the Stackelberg-population equilibrium response set and the Stackelberg-population equilibrium leader set by using the variational inequality technique and Brouwer’s fixed point theorem. We also show an existence theorem of Nash equilibrium for Stackelbergpopulation competition model under some mild conditions. Finally, we give an example to illustrate our main results.

Fractal analysis and control of the competition model

2016 ◽  
Vol 09 (03) ◽  
pp. 1650045 ◽  
Author(s):  
Mianmian Zhang ◽  
Yongping Zhang
Keyword(s):  
Feedback Control ◽  
Mathematical Models ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Julia Set ◽  
Julia Sets ◽  
Competition Model ◽  
Simulation Results ◽  
Population Competition ◽  
And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

scholarly journals Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

2020 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Fixed Point ◽  
Stationary Solution ◽  
Function Method ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Delayed Feedback ◽  
Competition Model ◽  
Numerical Examples ◽  
Unique Existence ◽  
Lyapunov Function Method

By partly generalizing the Lipschitz condition of existing results to the generalized Lipschitz one, the author utilizes a fixed point theorem, variational method and Lyapunov function method to derive the unique existence of globally asymptotical input-to-state stability of positive stationary solution for Gilpin-Ayala competition model with diffusion and delayed feedback under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of reaction-diffusion Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. And numerical examples illuminate the effectiveness and feasibility of the proposed methods.

scholarly journals Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces

2021 ◽  
Vol 14 (3) ◽  
pp. 650-665
Author(s):  
Tanakit Thianwan
Keyword(s):  
Fixed Point ◽  
Mixed Type ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Strong Convergence Theorem ◽  
Uniformly Convex ◽  
Mild Conditions ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

In this paper, a new mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings is constructed. We then establish a strong convergence theorem under mild conditions in a uniformly convex hyperbolic space. The results presented here extend and improve some related results in the literature.

scholarly journals Existence of solutions for impulsive fractional integrodifferential equations involving Gronwall’s inequality in Banach spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 115-122
Author(s):  
A. AL-OMARI ◽  
◽  
M. H. M. RASHID ◽  
K. KARTHIKEYAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Caputo Derivative ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Gronwall’S Inequality ◽  
Mild Conditions

In this paper, we study boundary value problems for impulsive fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

scholarly journals Social Responsibility Decision-Making of Universities in Stackelberg Competition

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Xiaolei Wang ◽  
Chaoqun Sun ◽  
Jiali Liu
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Social Responsibility ◽  
Competition Model ◽  
Competitive Position ◽  
Stackelberg Competition ◽  
The Government

This paper establishes a Stackelberg competition model of two universities considering social responsibility (SR) and market sensitivity (MS) and examines the equilibrium results of four different scenarios: only the leader implements SR; only the follower implements SR; both the leader and the follower implement SR; neither the leader nor the follower implements SR. Then, a comparative analysis is carried out on the influence of MS and SR level. The results show that the influence of MS depends on SR implementation instead of competitive position. If MS is sufficiently high, two universities have the motive to implement more SR; under different competition scenarios, universities make different SR decisions, but the leader and the government make the same decisions on the optimal SR level. Therefore, the government could encourage the leader to take SR first.

scholarly journals Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Zhangsong Yao ◽  
Yan-Kuen Wu ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iterative Algorithms ◽  
Fixed Point Problems ◽  
Variational Inclusions ◽  
Type Method ◽  
Common Solution ◽  
Mild Conditions

Iterative methods for solving variational inclusions and fixed-point problems have been considered and investigated by many scholars. In this paper, we use the Halpern-type method for finding a common solution of variational inclusions and fixed-point problems of pseudocontractive operators. We show that the proposed algorithm has strong convergence under some mild conditions.

STRONG CONVERGENCE OF IMPLICIT ITERATIVE ALGORITHMS FOR STRICTLY PSEUDO-CONTRACTIVE MAPPINGS

2021 ◽  
Vol 10 (8) ◽  
pp. 3023-3047
Author(s):  
M.O. Aibinu ◽  
S.C. Thakur ◽  
S. Moyo
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Contractive Mapping ◽  
Optical Illusion ◽  
Implicit Algorithm ◽  
Mild Conditions ◽  
Contractive Mappings

The class of strictly pseudo-contractive mappings is known to have more powerful applications than the class of nonexpansive mappings in solving nonlinear equations such as inverse and equilibrium problems. Motivated by the potency of the class of strictly pseudo-contractive mappings, a generalized viscosity implicit algorithm is constructed for finding their fixed points in the framework of Banach spaces. The strong convergence of the newly constructed sequence to a fixed point of a strictly pseudo-contractive mapping is obtained under some mild conditions on the parameters and the fixed point is shown to solve some variational inequality problems. An example is given to illustrate the convergence analysis of the newly constructed generalized viscosity implicit algorithm for the class of strictly pseudo-contractive mappings. The example also shows that the algorithm and the conditions which are imposed on the parameters are not just optical illusion.

scholarly journals Strong Convergence of an Iterative Algorithm for Hierarchical Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Poom Kumam ◽  
Thanyarat Jitpeera
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Variational Inequality Problem ◽  
Fixed Point Set ◽  
Mild Conditions ◽  
Hierarchical Problems ◽  
Point Set

We introduce the triple hierarchical problem over the solution set of the variational inequality problem and the fixed point set of a nonexpansive mapping. The strong convergence of the algorithm is proved under some mild conditions. Our results extend those of Yao et al., Iiduka, Ceng et al., and other authors.

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