In this paper, we first present some minimization theorems for a new class of nonnegative functionals defined on (q₁, q₂) -quasimetric spaces. We then apply these results to derive some new coincidence point and fixed point results for mappings in (q₁, q₂) -quasimetric spaces. In particular, we study sufficient conditions for the existence of coincidence points of a filling mapping and a Lipschitz mapping. Our results improve and generalize several results in the literature including those in Feng and Liu J. Math. Anal. Appl. , vol. 317, no. 1, 103–112 (2006), Arutyunov Dokl. Math. , vol. 76, no. 2, 665–668 (2007), Arutyunov and Gel’man Comput. Math. Math. Phys. , vol. 49, no. 7, 1111–1118 (2009), Fomenko Topol. Appl. , vol. 157, no. 4, 760–773 (2010) ; Moscow Univ. Math. Bull. , vol. 74, no. 6, 227–234 (2019), and Nguyen and Pasynkov Topol. Appl. , vol. 201, 57–77 (2016). Examples are also given to illustrate our results.
L. V. Nguyen (Thu,) studied this question.