  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 \'Swiatkowski,
Aran{\dj}elovi\'{c} and Ke\v{c}ki\'{c} and Alshehri, Aran{\dj}elovi\'c 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.
