Multistep-type construction of fixed point for multivalued ρ-quasi-contractive-like maps in modular function spaces

摘要

Purpose In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that PρT, an associate multivalued map, is a ρ-contractive-like mapping. Design/methodology/approach The concepts of relative ρ-stability and weak ρ-stability are introduced, and conditions in which these multistep iterations are relatively ρ-stable, weakly ρ-stable and ρ-stable are established for the newly introduced strong ρ-quasi-contractive-like class of maps. Findings Noor type, Ishikawa type and Mann type iterative sequences are deduced as corollaries in this study. Originality/value The results obtained in this work are complementary to those proved in normed and metric spaces in the literature.