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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.