Now showing items 1-10 of 36
On the Construction of a Norm Associated with the Measure of Noncompactness
(University of Texas at Arlington, 1976-02)
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 noncompactness corresponds to the norm in B(E). The results ...
On the Existence of Zeros of Lyapunov-Monotone Operators
(University of Texas at Arlington, 1975-02)
Consider a nonlinear operator T from a Banach space into itself. The study of the existence of zeros of T plays an important role in yielding fixed points of nonlinear operators. The operator T has a zero if and only if ...
The Method of Quasilinearization and Positivity of Solutions in Abstract Cones
(University of Texas at Arlington, 1976-03)
The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the method can be found in (Ref. 3). This method has been very ...
Existence and Comparison Results for Differential Equations in a Banach Space
(University of Texas at Arlington, 1974-07)
The study of the Cauchy problem for differential equations in a Banach space has taken two different directions. One direction is to find compactness type conditions that guarantee only existence of solutions and the ...
Monotone Method for Equations Describing Transport Phenomena in a Banach Space
(University of Texas at Arlington, 1981-06)
Existence of extremal solutions of initial and boundary value problems (B.V.P. for short) of differential equations in a Banach space has been recently considered in [2,7] by utilizing monotone iterative method. A ...
Monotone Iterative Technique for Delay Differantial Equations in Abstract Cones
(University of Texas at Arlington, 1982-04)
Monotone iterative technique is developed for delay differential equations in a Banach space by utilizing the method of upper and lower solutions.
Existence and Uniqueness of Solutions of Delay Differential Equations on a Closed Subset of a Banach Space
(University of Texas at Arlington, 1977-05)
In an earlier work , sufficient conditions for the existence of solutions in a closed subset F of a Banach space E for the Cauchy problem (1.1) [see pdf for notation] where [see pdf for notation], are obtained by ...
Fixed Point Theorms of Operators with PPF Dependence in Banach Spaces
(University of Texas at Arlington, 1975)
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] with range in a Banach space E denoted by [see pdf for ...
Fixed Point Theorem for Non-Expansive Mappings on Banach Spaces with Unifformly Normal Structure
(University of Texas at Arlington, 1977-11)
In  Kirk proved that if D is a bounded, closed, and convex subset of a reflexive Banach space that has normal structure, then every non-expansive mapping of D into D has a fixed point. This was also proved for a uniformly ...
Existence of Solutions of Boundary Value Problems for Nonlinear Second Order Systems in a Banach Space
(University of Texas at Arlington, 1977-03)
This paper is concerned with the existence of solutions of boundary value problems (BVP, for short) for nonlinear second order ordinary differential equations of the type (1.1) [see pdf for notation] (1.2) [see pdf for ...