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A Polynomial Dual of Partitions
(University of Texas at Arlington, 1974-09)
**Please note that the full text is embargoed** ABSTRACT: Let [see pdf for notation] be a non-negative integral polynomial.
The polynomial P(x) is m-graphical, and a multi-graph G a realization of P(x), provided there ...
Fixed Point Theorms of Operators with PPF Dependence in Banach Spaces
(University of Texas at Arlington, 1975)
**Please note that the full text is embargoed** ABSTRACT: In this paper we develop a theory of fixed points of a nonlinear operator, T, whose domain is the Banach space of continuous functions defined on an interval [a,b] ...
On the Zeros of Monotone Operators of Retarded Type in a Banach Space
(University of Texas at Arlington, 1975-09)
**Please note that the full text is embargoed** ABSTRACT: Recent interest in the Cauchy problem for differential equations in a Banach space [9] has stimulated a similar interest for differential equations of a retarded ...
Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones
(University of Texas at Arlington, 1975-06)
**Please note that the full text is embargoed** ABSTRACT: 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 ...
On the Construction of a Norm Associated with the Measure of Noncompactness
(University of Texas at Arlington, 1976-02)
**Please note that the full text is embargoed** ABSTRACT: It is shown that the bounded, nonempty subsets of a reflexive Banach space g can be imbedded in another Banach space B(E) in such a manner so that the measure of ...
Unitary Perfect Polynomials Over GF(q)
(University of Texas at Arlington, 1975-03)
**Please note that the full text is embargoed** ABSTRACT: For monic polynomials A(x), B(x) e GF[q,x], call B(x) a unitary divisor of A(x) provided (B(x),A(x)/B(x)) = 1 . The polynomial A(x) is called unitary perfect over ...
On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones
(University of Texas at Arlington, 1975-07)
**Please note that the full text is embargoed** ABSTRACT: In a recent paper, Petryshyn and Williamson [4] investigated the convergence of successive approximations of quasi-
nonexpansive mappings in a Banach space. This ...
The Extendability and Uniqueness of Solutions of Ordinary Differential Equations
(University of Texas at Arlington, 1976)
**Please note that the full text is embargoed** ABSTRACT: In a recent paper [1] the author obtained results on the extendability of solutions of perturbed differential equations. The question of the extendability of solutions ...
Lyapunov-like Vector Functions Using Pointwise Degenerate Systems as Comparison Functions
(University of Texas at Arlington, 1974-04)
**Please note that the full text is embargoed** ABSTRACT: The use of Lyapunov-like vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine ...
Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones
(University of Texas at Arlington, 1974-04)
**Please note that the full text is embargoed** ABSTRACT: As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by ...