Sahu, D. R. Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces. (English) Zbl 1123.47041 Commentat. Math. Univ. Carol. 46, No. 4, 653-666 (2005). Summary: We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach spaces. Our results improve various celebrated results of fixed point theory in the context of demicontinuity. Cited in 2 ReviewsCited in 47 Documents MSC: 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:asymptotically nonexpansive mapping; Banach contraction principle PDFBibTeX XMLCite \textit{D. R. Sahu}, Commentat. Math. Univ. Carol. 46, No. 4, 653--666 (2005; Zbl 1123.47041) Full Text: EuDML EMIS