Generalized suzuki-type mappings in modular vector spaces

Abstract

ABSTRACT Very recently, a new type of generalized nonexpansive mappings on Banach spaces was introduced as an extension for the nonexpansiveness condition of Suzuki. This paper adapts the new concept to modular spaces, successfully overcoming the problem of modulars having weaker properties than norms. The result consists in several fixed point-related outcomes. The modular nonexpansive mappings defined here also extends another recently developed concept, namely the modular Suzuki condition. An example is provided in order to prove the relevance of the concept defined in this paper.