This study focuses on the analysis of $C$-class functions, with particular attention given to the development of fixed-point theorems for mappings that satisfy $H$-$(\psi, \phi)$-contractive conditions. The principal aim is to extend fixed-point results to the broader framework of $G_{\mathcal{F}}$-complete metric spaces. This generalized setting provides greater flexibility of contractive mappings, covering cases not addressed by traditional fixed-point theory.
This paper studies the particular class of second order functional differential equations involving casual operators on a function space $L^p_{\mathrm{loc}}(\mathbb{R}_+, \mathbb{R}^n)$. Previous studies\cite{Corduneanu2008,Mahdavi2008} discussed this equations in the following different function spaces$C(\mathbb{R}_+,\mathbb{R}^n)$ and $L^2_{\mathrm{loc}}(\mathbb{R}_+,\mathbb{R}^n)$. We establish the existence and uniqueness of solutions for both linear and nonlinear cases. Our worked based on the resolvent kernel method, Hölder's inequality, and successive approximation techniques. Finally, We provide examples to illustrate our results.
Socialism and egalitarianism in the United States drew, among their principal sources of inspiration, on the work of the novelist Edward Bellamy. His utopian project, articulated in Looking Backward (1888) and Equality (1897), can be read as the outcome of prior experiences of intentional communities-mystical, Fourierist, and especially Owenite-combined with elements taken from republicanism and the North American democratic tradition. Recent theoretical developments in socialist republicanism make it possible to recast Bellamy's anticipations, particularly in a text of agitation and propaganda known as "The Parable of the Water Tank". This piece presents capitalism as a system of impersonal, objective, and political domination, while at the same time positing the self-emancipation of the working class and pointing toward a society-founded on cooperatives and radical democracy-which may be described as a social republic following the model set by the Paris Commune. After a succinct description of some original utopian experiments in the United States, Bellamy's parable is analyzed as well as some of the very early criticisms launched against it within the socialist field. Lastly, a reply-that intends to be a defense-is presented drawing from contemporary socialist republicanism.
The following paper aims to reflect on the exclusionary character of the Renaissance Republic of Venice. Famous for its great longevity, and stability-which earned it the title of serenissima-we argue that the perspectives of Niccol & ograve; Machiavelli and William Shakespeare allow us to elucidate its segregatory and expulsive character. Thus, through the works of the Florentine thinker and the English poet's comedy The Merchant of Venice, we seek to problematize the image of a Venice serenissima and the impossibility of a republic-whether more popular or more aristocratic-that would allow for a perfect ordering without exclusions or latent conflicts.
The relationship between Machiavelli and Lucretius is one of the most intriguing topics in contemporary interpretations of the Florentine thinker. Beginning with a brief overview of this encounter, we propose to follow Lucretius's lead to address-in discussion with J. G. A. Pocock's interpretation-the problem of political temporality in Machiavelli. Considering Machiavelli's analysis of the difference between the temporalities of the principality and the republic, we will propose a materialist reading of republican temporality to argue why this mode of political life is in better conditions to respond to the movement, mutation, and-more radically-the finitude of all political order. We will conclude with an analysis of the status of novelty, in which transformative forces and hopes for renewal enter into a critical tension in times of crisis.
