Common fixed point of generalized weakly contractive mappings on orthogonal modular spaces with applications

In this paper, we provide certain conditions under which guarantee the existence of a common fixed point for weakly contractive mappings defined on orthogonal modular spaces. Also, Banach fixed point theorem on an orthogonal modular space without completeness is obtained. To prove much stronger and more applicable results, some strong assumptions such as the convexity and the Fatou property of a modular are relaxed.