Fixed points of multivalued α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-admissible mappings and stability of fixed point sets in metric spaces

In this paper we establish some fixed point results of multivalued α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-admissible mappings in the framework of metric spaces. The mappings are assumed to satisfy certain rational type α-ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha {-}\psi $$\end{document}-contractions. We support our main results with an example. We use Hausdorff distance in our theorems. We also study the stability of fixed point sets of above mentioned set valued contractions. By applications of the multivalued results we obtain certain fixed point theorems of singlevalued mappings.