Abstract:
The cascade search principle for zeros of $(\alpha,\beta)$-search functionals and consequent fixed point and coincidence theorems are proved for collections of single-valued and set-valued mappings of $(b_1,b_2)$-quasimetric spaces. These results are extensions of some previous author's results in metric spaces. In particular, a generalization is obtained for some recent result on coincidences of a covering mapping and a Lipshitzian mappings of $(b_1,b_2)$-quasimetric spaces.
Key words:$(b_1,b_2)$-quasimetric space, $(\alpha,\beta)$-search functional, fixed point, coincidence point.
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