Weak contractive integral inequalities and fixed points in modular metric spaces

• Main Authors: Nawab Hussain, Marwan A Kutbi, Nazra Sultana, Iram Iqbal
• Format: Article
• Language: English
• Published: SpringerOpen 2016-03-01
• Series: Journal of Inequalities and Applications
• Subjects: modular metric space; fixed point; ω-weakly compatible maps
• Online Access: http://link.springer.com/article/10.1186/s13660-016-1032-1

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.