Novel results on fixed-point methodologies for hybrid contraction mappings in $ M_{b} $-metric spaces with an application

Abstract

By combining the results of Wardowski's cyclic contraction operators and admissible multi-valued mappings, the motif of $ \eta $-cyclic $ \left(\alpha _{\ast }, \beta _{\ast }\right) $-admissible type $ \digamma $-contraction multivalued mappings are presented. Moreover, some novel fixed point theorems for such mappings are proved in the context of $ M_{b} $-metric spaces. Also, two examples are given to clarify and strengthen our theoretical study. Finally, the existence of a solution of a pair of ordinary differential equations is discussed as an application.

Keywords

• fixed point methodology
• m_b-metric space
• η-cyclic (α_∗，β_∗)-admissible ϝ-contraction multivalued mapping