Generalized suzuki-type mappings in modular vector spaces. (1st September 2020)

• Record Type: Journal Article
• Authors: Bejenaru, Andreea; Postolache, Mihai
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 2177
• Page End: 2198
• Publication Date: 2020-09-01
• Subjects: Modular vector space -- (α, β)-Suzuki-type mapping -- iterative process -- T-Opial condition; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1647202
• Languages: English
• ISSNs: 0233-1934

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.