Fixed Point Theorems of Generalized Contractions in Partially Ordered Cone Metric Spaces

TL;DR

This paper establishes fixed point theorems for generalized contractions in complete cone metric spaces with partial orders, extending previous results from metric to cone metric spaces and providing broader applicability.

Contribution

It generalizes fixed point theorems for generalized contractions to cone metric spaces with partial orders, expanding their scope beyond traditional metric spaces.

Findings

Fixed point theorems for generalized contractions in cone metric spaces.

Extension of previous theorems from metric to cone metric spaces.

Applications to differential equations.

Abstract

The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani, K. Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Analysis 72 (2010) 1188-1197] from metric spaces to cone metric spaces.