Some novel fixed point theorems in partially ordered metric spaces

Abstract

Our aim in this communication is to present a new type of contraction and common fixed point results for non-continuous self mappings without using the compatibility and commutative property. Moreover, we have found common fixed point without using the Cauchy’s criterion for convergence. Some illustrative examples with graphical representation and remarks are given to justify that the contraction introduced in the main result is new and unique, which will be useful for future researches.

Keywords

• fixed point
• continuity
• compatibility
• contraction
• partially ordered metric spaces