In this paper, we prove a general fixed point theorem in $textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $textrm{S}$-metric spaces.

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].

A discourse containing one or more sentences describes daily issues and events for people to communicate their thoughts opinions. As are normally consist of multiple text segments, correct understanding the theme a should take into consideration relations in between segments. Although sometimes connective exists raw texts conveying relations, it is often cases that no two segments but some impl...

Implicit discourse relation recognition is a challenging task due to the absence of necessary informative clues from explicit connectives. An implicit recognizer has carefully tackle semantic similarity sentence pairs and severe data sparsity issue. In this article, we learn token embeddings encode structure dependency point view in their representations use them initialize baseline model make ...

The paper deals with the Darboux problem for the equation Dxyz(x, y) = f(x, y, z(x,y)) where z(x,y) is a function defined by z(x,y)(t, s) = z(x + t, y + s), (t, s) ∈ [−a0, 0]× [−b0, 0]. We construct a general class of difference methods for this problem. We prove the existence and uniqueness of solutions to implicit functional difference equations by means of a comparison method; moreover we gi...

Implicit discourse relation recognition is a challenging task in the natural language processing field, but important to many applications such as question answering, summarizat ion and so on. Previous research used either art ificially created implicit discourse relat ions with connectives removed from explicit relations or annotated implicit relat ions as training data to detect the possible ...

1. Introduction. This note presents a few of the results which we have obtained by applying a classical and fundamental idea to the analysis of certain partial difference equations. The idea is that certain multidimensional problems can be solved by solving a few one-dimensional problems—it is the basis of the classical method of separation of variables of mathematical physics. In the case of p...

Implicit discourse relation classification is of great challenge due to the lack of connectives as strong linguistic cues, which motivates the use of annotated implicit connectives to improve the recognition. We propose a feature imitation framework in which an implicit relation network is driven to learn from another neural network with access to connectives, and thus encouraged to extract sim...

In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and  the common property (E.A.) in   modified  intuitionistic probabilistic metric spaces.Then, by the commonproperty (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.