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Fixed Point Theorems on Closed Sets Through Abstract Cones
(University of Texas at Arlington, 1976-03)
Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of an iterative sequence whose limit is a fixed point in D. ...
Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones
(University of Texas at Arlington, 1975-06)
The contraction mapping principle and the Schauder principle can both be viewed as a comparison of maps. For the former one has a condition of the type [see pdf for notation] and for the latter one has a condition of the ...
Fixed Point Theorems Through Abstract Cones
(University of Texas at Arlington, 1974-03)
A well-known theorem of Banach states that if T is a mapping on a complete metric space [see pdf for notation] such that for some number [see pdf for notation], the inequality (1.1) [see pdf for notation] holds, then T has ...