Fixed point theorems for generalized weak integral contractive condition

In the present work, we establish the existence of common fixed points for pairs of subsequential continuous mappings and variants of sequential continuous mappings as well as variants of R−weak commuting mappings, non-compatible and faintly compatible mappings satisfying a generalized ()-weak integral contractive condition involving cubic terms of distance functions. We also discuss the existence and uniqueness of common solution for a system of functional equations arising in the dynamic programming.