Injective envelopes of transition systems and Ferrers languages

We consider reflexive and involutive transition systems over an ordered alphabet $A$ equipped with an involution. We give a description of the injective envelope of any two-element set in terms of Galois lattice, from which we derive a test of its finiteness. Our description leads to the notion of Ferrers language.Comment: 23 page

Big data traffic management in vehicular ad-hoc network

Today, the world has experienced a new trend with regard to data system management, traditional database management tools have become outdated and they will no longer be able to process the mass of data generated by different systems, that's why big data is there to process this mass of data to bring out crucial information hidden in this data, and without big data technologies the treatment is very difficult to manage; among the domains that uses big data technologies is vehicular ad-hoc network to manage their voluminous data. In this article, we establish in the first step a method that allow to detect anomalies or accidents within the road and compute the time spent in each road section in real time, which permit us to obtain a database having the estimated time spent in all sections in real time, this will serve us to send to the vehicles the right estimated time of arrival all along their journey and the optimal route to attain their destination. This database is useful to utilize it like inputs for machine learning to predict the places and times where the probability of accidents is higher. The experimental results prove that our method permits us to avoid congestions and apportion the load of vehicles in all roads effectively, also it contributes to road safety

Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph

We extend the result of Kirk-Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi’s fixed point theorem. Some concrete examples are given to support the obtained results

Injective envelopes of transition systems and Ferrers languages

We consider reflexive and involutive transition systems over an ordered alphabet A equipped with an involution. We give a description of the injective envelope of any two-element set in terms of Galois lattice, from which we derive a test of its finiteness. Our description leads to the notion of Ferrers language

Common Fixed-Point Theorems in Modular Function Spaces Endowed with Reflexive Digraph

The purpose of this work is to extend the Knaster–Tarski fixed-point theorem to the wider field of reflexive digraph. We give also a DeMarr-type common fixed-point theorem in this context. We then explore some interesting applications of the obtained results in modular function spaces

Fixed Point Results for C-Contractive Mappings in Generalized Metric Spaces with a Graph

In this paper, we establish fixed point theorems for Chatterjea contraction mappings on a generalized metric space endowed with a graph. Our results extend, generalize, and improve many of existing theorems in the literature. Moreover, some examples and an application to matrix equations are given to support our main result

Some Fixed Point Theorems in Modular Function Spaces Endowed with a Graph

The aim of this paper is to give fixed point theorems for G-monotone ρ-nonexpansive mappings over ρ-compact or ρ-a.e. compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work

A Study of a Nonlinear Ordinary Differential Equation in Modular Function Spaces Endowed with a Graph

In this paper, we prove by means of a fixed-point theorem an existence result of the Cauchy problem associated to an ordinary differential equation in modular function spaces endowed with a reflexive convex digraph

Free monoids and generalized metric spaces

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