Yang, Shu Lang Quasidifferentiability and positive solutions of equations for set-valued mappings. (English) Zbl 0867.47037 Nonlinear Anal., Theory Methods Appl. 25, No. 5, 487-498 (1995). From the text: “In this paper, the quasidifferentiability and the quasiderivative of set-valued mappings are introduced and applied to the study of problems concerning the positive solution of equations and the positive (relative) eigenvector and eigenvalue for the set-valued \(k\)-set contraction with \(k\) in \([0,1)\) in a \((B)\)-space with a cone. And improvements and developments of the results on the positive fixed point theorems for the Fréchet differentiable or the semidifferentiable (single-valued) completely continuous mappings or strict set contraction for Petryshyn, Amann, Edmunds et al. and the author are obtained in this paper”. Reviewer: S.L.Singh (Rishikesh) MSC: 47H04 Set-valued operators 47H10 Fixed-point theorems 54C60 Set-valued maps in general topology 46G05 Derivatives of functions in infinite-dimensional spaces 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 49J50 Fréchet and Gateaux differentiability in optimization 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces Keywords:quasidifferentiability; quasiderivative; set-valued mappings; positive solution; positive (relative) eigenvector; set-valued \(k\)-set contraction; \((B)\)-space with a cone; Fréchet differentiable; semidifferentiable PDFBibTeX XMLCite \textit{S. L. Yang}, Nonlinear Anal., Theory Methods Appl. 25, No. 5, 487--498 (1995; Zbl 0867.47037) Full Text: DOI References: [1] Petryshyn, W. V., J. math. Analysis Applic., 133, 297-305 (1988) [2] Amann, H., SIAM Rev., 18, 620-709 (1976) [3] Amann, H., J. fund. Analysis, 14, 162-171 (1973) [4] Edmunds, D. E.; Potter, A. J.; Stuart, C. A., (Proc. R. Soc. London Sr.A., 328 (1972)), 67-81 [5] Yang, Sh. L., Chin. Ann. Math., 7A, 705-708 (1986) [6] Yang, Sh. L., J. sys. Sci. math. Sci., 7, 329-334 (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.