Multi-valued F-contractions and the solution of certain functional and integral equations

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results

Marketing strategy, social responsibility, and value chain in the agri-food system

The agri-food sector has changed significantly over the years, moving from a simple production system to a more and more industrialized one. For agents/operators involved in this sector, ensuring product quality and environmental externalities has become the key point to gaining a competitive advantage. In this context, corporate social responsibility (CSR) fits perfectly. This study analyzes the influence of CSR practices on the economic performance of a random sample of 130 agri-food companies in Italy. The results of an analysis of multiple linear regression models show that the economic performance (measured through value added and income) of agri-food enterprises seems to be influenced statistically by workplace CSR practices. Analysis of another model, during which we studied the relationship between income and the CSR practices (independent variables), highlights that operating results (economic performance) can be improved by CSR practices regarding the workplace, environment, and local community. Thus, empirical evidence shows that some CSR practices have positive effects on economic performance, with several implications for theory and practice

A Reinforcement Learning Approach to the Design of Quantum Chains for Optimal Energy Transfer

We propose a bottom-up approach, based on Reinforcement Learning, to the design of a chain achieving efficient excitation-transfer performances. We assume distance-dependent interactions among particles arranged in a chain under tight-binding conditions. Starting from two particles and a localised excitation, we gradually increase the number of constitutents of the system so as to improve the transfer probability. We formulate the problem of finding the optimal locations and numbers of particles as a Markov Decision Process: we use Proximal Policy Optimization to find the optimal chain-building policies and the optimal chain configurations under different scenarios. We consider both the case in which the target is a sink connected to the end of the chain and the case in which the target is the right-most particle in the chain. We address the problem of disorder in the chain induced by particle positioning errors. We are able to achieve extremely high excitation transfer in all cases, with different chain configurations and properties depending on the specific conditions.Comment: 8 pages, 6 figure

Fixed points of dynamic processes of set-valued F-contractions and application to functional equations

The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via the dynamic processes. The paper includes a non-trivial example which shows the motivation for such investigations. The work is summarized by the application of the introduced nonlinear F-contractions to functional equations