Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 11 1 2020 04 01 The new results in extended $b$-metric spaces and applications 473 482 4361 10.22075/ijnaa.2019.18239.1998 EN Zoran Mitrovic Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam Huseyin Işık Department of Mathematics, Mus Alparslan University, 49250 Mus, Turkey Stojan Radenovic Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia Journal Article 2019 07 10 In this paper, we give a proof of the results of Miculescu and Mihail [J. Fixed Point Theory Appl. 19, 2153-2163 (2017)] and Suzuki [J. Inequal. Appl. 2017, Paper No. 256, 11 p.] in extended $b$-metric spaces. Also we give some applications of our result. Fixed point b-metric space Multi-valued mapping https://ijnaa.semnan.ac.ir/article_4361_eb773e2f157a603f268f0b4901f84a12.pdf