# Inequalities for the modified k-Bessel function

## TL;DR

This paper investigates inequalities and monotonicity properties of the generalized k-Bessel functions, including their ratios and log-convexity, providing new insights into their mathematical behavior.

## Contribution

It introduces new monotonicity and convexity results for the generalized k-Bessel functions and their ratios, expanding understanding of their inequalities.

## Key findings

- Monotonicity of the ratio of different order k-Bessel functions
- Log-convexity of the k-Bessel functions with respect to order
- Monotonicity of the ratio between k-Bessel and k-confluent hypergeometric functions

## Abstract

The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the m-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.