Some fixed points results for extended nonlinear contractions defined on $d-CS$ spaces
In this paper we shall introduced the class of $d-CS$ spaces and so we shall obtained topological approach to large Kasahara spaces. This class include complete symmetric spaces, complete quasi $b$-metric spaces and complete $b$-spaces, but not include $d^*$-complete topological spaces and $d$-complete topological spaces. Further will be presented fixed theorem for nonlinear extended-contraction defined on this spaces, which generalize earlier results obtaned by Browder, Matkowski, Jachymski, Matkowski and Światkowski, Aranđelović and Kečkić and Alshehri, Aranđelović and Shahzad. Also, we obtain the fixed point theorem for nonlinear extended-contraction defined on quasi-metric spaces which extended recent result's of Pasicki, obtained for pseudo-metric spaces.