scholarly journals Modular coinduction up-to for higher-order languages via first-order transition systems

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Jean-Marie Madiot ◽  
Damien Pous ◽  
Davide Sangiorgi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Lambda Calculus ◽  
Point Theory ◽  
Transition Systems ◽  
First Order ◽  
Comprehensive Theory ◽  
Pi Calculus ◽  
First Order Transition ◽  
Large Corpus

The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references.

scholarly journals Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Lower Solution ◽  
Existence Of Solution ◽  
Order Ordinary Differential Equation ◽  
Complete Metric Spaces ◽  
First Order ◽  
Contractive Mappings

We establish a fixed point theorem withw-distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.

scholarly journals An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1183
Author(s):  
Adrian Nicolae Branga ◽  
Ion Marian Olaru
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Linear Differential Equations ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Linear Differential

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.

scholarly journals Fixed point theorems via w-distance in relational metric spaces with an application

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1889-1898
Author(s):  
Gopi Prasad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Binary Relation ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
First Order ◽  
Contractive Mappings

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance on metric spaces endowed with an arbitrary binary relation. Our fixed point theorems generalize recent results of Senapati and Dey [ J. Fixed Point Theory Appl., 19, 2945-2961, (2017)] and many other important results of the existing literature. Moreover, in order to revel the usability of our findings an example and an application to first order periodic boundary value problem are given.

scholarly journals Exact Multiplicity of Solutions for a Class of Singular Generalized One-Dimensionalp-Laplacian Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Youwei Zhang
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Point Theory ◽  
One Dimensional ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Exact Multiplicity Of Solutions ◽  
Exact Multiplicity

We describe the existence of positive solutions for a class of singular generalized one-dimensionalp-Laplacian problem. By applying the related fixed point theory in cone, some new and general results on the existence of positive solutions to the singular generalizedp-Laplacian problem are obtained. Note that the nonlinear termfinvolves the first-order derivative explicitly.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method
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