scholarly journals Multi-leader-follower potential games

2021 ◽  
Vol 71 ◽  
pp. 155-162
Author(s):  
Sonja Steffensen
Keyword(s):  
Sufficient Conditions ◽  
Potential Games ◽  
Future Research ◽  
Potential Game ◽  
Nash Games ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Numerical Solution Methods ◽  
Starting Point ◽  
Solution Methods

In this paper, we discuss a particular class of Nash games, where the participants of the game (the players) are divided into two groups (leaders and followers) according to their position or influence on the other players. Moreover, we consider the case, when the leaders’ and/or the followers’ game can be described as a potential game. This is a subclass of Nash games that has been introduced by Monderer and Shapley in 1996 and has beneficial properties to reformulate the bilevel Nash game. We develope necessary and sufficient conditions for Nash equilibria and present existence and uniqueness results. Furthermore, we discuss some Examples to illustrate our results. In this paper, we discussed analytical properties for multi-leader follower potential games, that form a subclass of hierarchical Nash games. The application of these theoretical results to various fields of applications are a future research topic. Moreover, they are meant to serve as a starting point for the developement of efficient numerical solution methods for multi-leader-follower games.

scholarly journals ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (5) ◽  
pp. 604-618 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Guotao Wang ◽  
Bashir Ahmad ◽  
Lihong Zhang ◽  
Aatef Hobiny ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Given

In this paper, we discuss the existence of solutions for nonlinear qdifference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal solutions for the given problem are established. The results are well illustrated with the aid of examples.

scholarly journals Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ameth Ndiaye ◽  
Fulgence Mansal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Ulam Stability ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Fixed Point Theorem ◽  
Banach Principle ◽  
Stability Of The Solution

In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.

scholarly journals Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 927 ◽  
Author(s):  
Akbar Zada ◽  
Shaheen Fatima ◽  
Zeeshan Ali ◽  
Jiafa Xu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Stability Results ◽  
Theoretical Results

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

scholarly journals On nonlinear pantograph fractional differential equations with Atangana–Baleanu–Caputo derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed S. Abdo ◽  
Thabet Abdeljawad ◽  
Kishor D. Kucche ◽  
Manar A. Alqudah ◽  
Saeed M. Ali ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence And Uniqueness Results ◽  
Gronwall’S Inequality ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we obtain sufficient conditions for the existence and uniqueness results of the pantograph fractional differential equations (FDEs) with nonlocal conditions involving Atangana–Baleanu–Caputo (ABC) derivative operator with fractional orders. Our approach is based on the reduction of FDEs to fractional integral equations and on some fixed point theorems such as Banach’s contraction principle and the fixed point theorem of Krasnoselskii. Further, Gronwall’s inequality in the frame of the Atangana–Baleanu fractional integral operator is applied to develop adequate results for different kinds of Ulam–Hyers stabilities. Lastly, the paper includes an example to substantiate the validity of the results.

scholarly journals New Conditions of The Existence of Fixed Point in Δ- Ordered Δ Banach Algebra

2020 ◽  
Vol 18 ◽  
pp. 60-71
Author(s):  
Boushra Hussein
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Hausdorff Space ◽  
Sufficient Conditions ◽  
Main Idea ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
New Space ◽  
Necessary And Sufficient ◽  
Ordered Banach Algebra

The main idea is to construct a new algebra and find new necessary and sufficient conditions equivalent to the existence of a fixed point. In this work, an algebra is constructed, called Δ - ordered Banach algebra, we define convergent in this new space, Topological structure on  Δ ordered Banach Algebra and prove this as Hausdorff space. Also, we define new conditions as Δ- lipshtiz,, Δ- contraction  contraction , in this algebra construct, we prove this condition is the existence and uniqueness results of the fixed point. In this paper,  we prove a common fixed point if the self-functions satisfy the new condition which is called Ф-contraction.  

scholarly journals Uniqueness and Existence of Positive Solutions for Singular Differential Systems with Coupled Integral Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yujun Cui ◽  
Lishan Liu ◽  
Xingqiu Zhang
Keyword(s):  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary ◽  
Monotone Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Existence Of Positive Solutions ◽  
Integral Boundary Value Problems

This paper provides sufficient conditions for the existence and uniqueness of positive solutions to a singular differential system with integral boundary value. The emphasis here is that the boundary conditions are coupled and this is where the main novelty of this work lies. By mixed monotone method, the existence and uniqueness results of the problem are established. An example is given to demonstrate the main results.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals Consumer Neuroscience Techniques in Advertising Research: A Bibliometric Citation Analysis

2021 ◽  
Vol 13 (3) ◽  
pp. 1589
Author(s):  
Juan Sánchez-Fernández ◽  
Luis-Alberto Casado-Aranda ◽  
Ana-Belén Bastidas-Manzano
Keyword(s):  
Self Report ◽  
Future Research ◽  
Complex Nature ◽  
Clear Understanding ◽  
Continuous Growth ◽  
Main Research ◽  
Consumer Neuroscience ◽  
Starting Point ◽  
Wide Range ◽  
Performance Analysis Tools

The limitations of self-report techniques (i.e., questionnaires or surveys) in measuring consumer response to advertising stimuli have necessitated more objective and accurate tools from the fields of neuroscience and psychology for the study of consumer behavior, resulting in the creation of consumer neuroscience. This recent marketing sub-field stems from a wide range of disciplines and applies multiple types of techniques to diverse advertising subdomains (e.g., advertising constructs, media elements, or prediction strategies). Due to its complex nature and continuous growth, this area of research calls for a clear understanding of its evolution, current scope, and potential domains in the field of advertising. Thus, this current research is among the first to apply a bibliometric approach to clarify the main research streams analyzing advertising persuasion using neuroimaging. Particularly, this paper combines a comprehensive review with performance analysis tools of 203 papers published between 1986 and 2019 in outlets indexed by the ISI Web of Science database. Our findings describe the research tools, journals, and themes that are worth considering in future research. The current study also provides an agenda for future research and therefore constitutes a starting point for advertising academics and professionals intending to use neuroimaging techniques.

scholarly journals Application of the Socio-Ecological System Framework to Forest Fire Risk Management: A Systematic Literature Review

2021 ◽  
Vol 13 (4) ◽  
pp. 2121 ◽  
Author(s):  
Ingrid Vigna ◽  
Angelo Besana ◽  
Elena Comino ◽  
Alessandro Pezzoli
Keyword(s):  
Risk Management ◽  
Community Involvement ◽  
Forest Ecosystems ◽  
Local Community ◽  
Fire Risk ◽  
Future Research ◽  
Specific Reference ◽  
Clear Understanding ◽  
Wildfire Risk ◽  
Starting Point

Although increasing concern about climate change has raised awareness of the fundamental role of forest ecosystems, forests are threatened by human-induced impacts worldwide. Among them, wildfire risk is clearly the result of the interaction between human activities, ecological domains, and climate. However, a clear understanding of these interactions is still needed both at the global and local levels. Numerous studies have proven the validity of the socioecological system (SES) approach in addressing this kind of interdisciplinary issue. Therefore, a systematic review of the existing literature on the application of SES frameworks to forest ecosystems is carried out, with a specific focus on wildfire risk management. The results demonstrate the existence of different methodological approaches that can be grouped into seven main categories, which range from qualitative analysis to quantitative spatially explicit investigations. The strengths and limitations of the approaches are discussed, with a specific reference to the geographical setting of the works. The research suggests the importance of local community involvement and local knowledge consideration in wildfire risk management. This review provides a starting point for future research on forest SES and a supporting tool for the development of a sustainable wildfire risk adaptation and mitigation strategy.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

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