New Multi-valued Contractions with Applications in Dynamic Programming

Abstract

In this paper, two well-celebrated results in metric fixed point theory due to Jaggi and DassGupta are revisited. To this end, the concepts of Jaggi and Dass-Gupta type bilateral multivalued contractions are introduced and suitable conditions for existence of fixed points for such mappings are established. A nontrivial example is provided to support the hypotheses of our main results. Moreover, a few consequences which dwell upon the generality of the ideas presented herein are pointed out and discussed. Finally, one of our theorems is applied to investigate sufficient conditions for existence of solutions of nonlinear functional equations arising in dynamic programming and in optimization theory.