Zeros of Multi-Valued Functionals in Metric Spaces with Applications

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.