James type constants and fixed points for multivalued nonexpansive mappings

In this paper, we give some sufficient conditions for the Domínguez–Lorenzo condition in terms of the James type constant JX,t(τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{X,t}(\tau )$$\end{document}, the coefficient of weak orthogonality μ(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu (X)$$\end{document} and the Domínguez Benavides coefficient R(1, X), which imply the existence of fixed points for multivalued nonexpansive mappings. Our results extend some well known results in the recent literature.