Existence results for the families of multi-mappings with applications to integral and functional equations

Abstract

Abstract The aim of this manuscript is to prove some new fixed-point results for the two families of multivalued dominated-contractive maps defined on a closed ball in a complete multiplicative-metric space. The fixed-point theorems for multigraph-dominated maps are established. We also investigate the existence of fixed points of the two families of graphic contractions in a multiplicative-metric space. For illustration, an example is provided to clarify that the hypothesis of the obtained result is valid. Moreover, the applications of the obtained results to show the existence of solutions to the coupled systems of nonlinear Volterra-type integral equations and mappingal equations are presented as a confirmation of the novelty of our results.

Keywords

• Generalized F-contraction
• Closed ball
• α ∗ $\alpha _{\ast }$ -dominated multivalued maps
• Graphical contraction
• Integral and mapping equations