# Inequalities of extended (p,q)-beta and confluent hypergeometric function

## TL;DR

This paper investigates the mathematical properties of extended (p,q)-beta and confluent hypergeometric functions, establishing their log-convexity, monotonicity, and Turán type inequalities to deepen understanding of their behavior.

## Contribution

It introduces new inequalities and properties for extended (p,q)-beta and confluent hypergeometric functions, expanding the theoretical framework of these special functions.

## Key findings

- Proved log-convexity of extended (p,q)-beta functions
- Established Turán type inequalities for these functions
- Analyzed monotonicity properties of extended (p,q)-confluent hypergeometric functions

## Abstract

In this present paper, we establish the log-convexity and Tur\'an type inequalities of extended $(p,q)$-beta functions. Also, we present the log-convexity, the monotonicity and Tur\'an type inequalities for extended $(p,q)$-confluent hypergeometric function by using the inequalities of extended $(p,q)$-beta functions.