Fixed point for variants of compatible mappings satisfying weak contraction involving cubic terms of metric function

In this paper, we prove some common fixed point theorems for pairs of compatible mappings of type (R), (K) and (E) satisfying weak contraction condition that involves cubic terms of metric function. As applications, we discuss the existence and uniqueness of common solutions for a class of the functional equations in dynamic programming.

Automated summary

This paper proves some common fixed point theorems for pairs of compatible mappings of specific types, while discussing the existence and uniqueness of common solutions for a class of functional equations in dynamic programming.