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Statistical convergence of sequences of sets

Nuray F, Rhoades B. E.

Fasciculi Mathematici

2012

Nr 49

87--99

The concept of convergence of sequences of points has been extended by several authors to convergence of sequences of sets. The three such extensions that we will consider in this paper are those of Kuratowski, Wijsman and Hausdorff. We shall define statistical convergence for sequences of sets and establish some basic theorems, thereby obtaining generalizations of the corre-sponding results for statistical convergence of sequences of points.

Some weakly contractive mapping theorems in partially ordered spaces and applications

Rhoades B. E., Pathak H. K., Mishra S. N.

Demonstratio Mathematica

2012

Vol. 45, nr 3

621-636

The purpose of this paper is to present some fixed point theorems for certain weakly contractive mappings, known as weakly (…)-contractive mappings, in a complete metric space endowed with a partial ordering. Subsequently, we apply our main results to obtain a solution of a first order periodic problem and study the possibility of optimally controlling the solutions of ordinary differential equations via dynamic programming.