Abstract:
In this paper we introduce the notion of nonlinear search functionals in metric spaces and establish the existence of zeros for such functionals. We also present a theorem on the preservation of the existence of zeros of a one-parameter family of nonlinear search functionals. These results are then applied to derive some fixed point and coincidence point results for both single-valued and set-valued mappings. An illustrative example is provided to support our finding.
Keywords:multi-valued search functional, family of multi-valued functionals, coincidence point, fixed point.
