# Fixed points of multivalued convex contractions with application

## TL;DR

This paper extends fixed point theory for convex contractions in b-metric spaces and applies it to solve a nonlinear integral equation.

## Contribution

The paper introduces new fixed point results for multivalued convex contractions and applies them to a nonlinear Fredholm integral equation.

## Key findings

- Fixed point outcomes are established for single-valued convex contraction mappings in b-metric spaces.
- A new result for multivalued convex contractions is derived, analogous to Nadler’s fixed point theorem.
- The results are applied to solve a nonlinear Fredholm integral equation using a Chatterjea convex contraction.

## Abstract

In this work, we establish fixed point outcomes for single- valued convex contraction type mappings in the context of a b-metric space. Some of the new results are extended for a multivalued convex contraction and an F-convex contraction. Thereby, an analogue of the famous Nadler’s fixed point theorem for a multivalued convex contraction mapping is obtained. The relation among various contractions is presented in a diagram for an insight in this area of investigations. We apply a special case of Theorem 2.11, to solve a nonlinear Fredholm integral equation for a Chatterjea convex contraction.