doiSerbia

Simulation type functions and coincidence points

Radenović Stojan (Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam + Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)
Chandok Sumit (School of Mathematics, Thapar University, Patiala, India)

In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [American Math. Monthly 83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015) 345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].

Keywords: Point of coincidence, Common fixed point, Compatible mappings, Commuting mappings, Simulation function, C-class function, Property CF