Abstract
Branciari (Int. J. Math. Math. Sci. 29(9):531-536,
2002
) gave an interesting supplement of Banach’s contraction principle for an integral-type inequality. In this paper, we introduce different notions of generalized
ω
-weak contractive inequalities of integral type in modular metric spaces and prove the presence and uniqueness of common fixed points for such contractions under
ω
-weak compatibility of underlying maps. Our results generalize and extend the results of Azadifar
et al.
(J. Inequal. Appl. 2013:483,
2013
), Liu
et al.
(Fixed Point Theory Appl. 2013:2672013,
2013
), Beygmohammadi and Razani (Int. J. Math. Math. Sci. 2010: Article ID 317107,
2010
), and many others. Moreover, an example is provided here to demonstrate the applicability of the obtained results.