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Now showing items 1-10 of 10

#### 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 a Boundary Value Problem for a Class of Differential Equations with a Deviating Argument

(University of Texas at Arlington, 1973-10)

Recently, J. Chandra [1] obtained comparison estimates for differential equations with deviating argument
(1) [see pdf for notation]
on the interval I: to [see pdf for notation] , where [see pdf for notation] is a given ...

#### 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. ...

#### On the Existence of Solutions of Differential Equations in a Banach Space

(University of Texas at Arlington, 1974-03)

The study of Cauchy problem for differential equations in a Banach space has taken two different directions. One approach is to find compactness type conditions [1,2,4,9,14] to guarantee existence of solutions only and the ...

#### Differential Inequalities and Flow-Invariance via Linear Functionals

(University of Texas at Arlington, 1977-05)

This paper deals with flow-invariance properties with respect to [see pdf for notation] and resulting comparison inequalities. Both the order relation He and the regularity conditions on x are defined, in a general manner, ...

#### 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 ...

#### On a Measure of Nonconvexity and Applications

(University of Texas at Arlington, 1975-06)

The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that regard was not appreciated until much later). Following ...

#### Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point

(University of Texas at Arlington, 1973-12)

Consider the equation (1.1) [see pdf for notation]
on a Hilbert space H. Here n is a scalar and [see pdf for notation] is a linear Fredholm operator. That is:
(a) L is closed; (b) The domain, D(L) is dense in H;
(c) 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 ...

#### Comparison Principle and Non Linear Contract in Abstract Spaces

(University of Texas at Arlington, 1973-10)

The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they make use of partial orderings and maximal solutions; concepts ...