# Numerous inequalities and related communications accompanying discrete divergence models in probability spaces

## TL;DR

This paper explores inequalities in probability spaces to improve communication systems and information transfer efficiency.

## Contribution

A general divergence model is introduced, extending information-theoretic inequalities and results.

## Key findings

- Various inequalities for finite sequences of positive real numbers were built.
- Important communications concerning positive real numbers and divergence models were derived.
- The model has implications for designing reliable and secure communication systems.

## Abstract

The analysis of inequalities aids in the formulation of optimal coding schemes that improve the rate of information transfer while reducing the probability of errors. This consequently implies that we have a major impact on having solid and secured correspondence systems for applications running from broadcast communications to information pressure. Information theory inequalities constitute a theoretical toolbox for designing channels that can overcome a challenging environment, allowing information to be held and communicated reliably and securely in a world that is becoming ever more interconnected. The paper introduces a general divergence model in general probability spaces and extends known information-theoretic inequalities and results based on variational models. We have built various inequalities for finite sequences of positive real numbers, the specific cases of which are important in information theory, especially in connection with several divergence models that remain in the literature. Additionally, we have derived certain other important communications concerning positive real numbers in relation to some divergence models.