A novel study for hybrid pair of multivalued dominated mappings in b-multiplicative metric space with applications

Abstract

Abstract The aim of this paper is to prove some new fixed point results for a pair of multivalued dominated locally contractive mappings in b-multiplicative metric space. Further, fixed point theorems for multigraph-dominated mappings are also established. Some new fixed point results on a closed ball are obtained for a pair of multigraph-dominated mappings endowed with graphic structure in b-multiplicative metric space. An illustrative example is given to show the validity of the hypothesis of our obtained result. Moreover, applications for a coupled system of nonlinear Volterra-type integral equations and functional equations in dynamic programming are presented to show the novelty of our results.

Keywords

• Fixed point
• Generalized F-contraction
• Closed ball
• α ∗ $\alpha _{\ast }$ -dominated multivalued mappings
• Graph contraction
• Integral equations