Best proximity pair and fixed point results for noncyclic mappings in modular spaces

• Published in: Arab journal of mathematical sciences Vol. 24; no. 2; pp. 147 - 165
• Main Authors: Chaira, Karim, Lazaiz, Samih
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2018; Emerald Publishing
• Subjects: [formula omitted]-admissible sets; [formula omitted]-normal structure; Best proximity pair; Modular spaces; Relatively [formula omitted]-nonexpansive mappings; Relatively ρ-nonexpansive mappings; ρ-normal structure; 41A65; 47H09; Best proximity pair; ρ-admissible sets; Modular spaces
• ISSN: 1319-5166
• DOI: 10.1016/j.ajmsc.2018.02.002

In this paper, we formulate best proximity pair theorems for noncyclic relatively ρ-nonexpansive mappings in modular spaces in the setting of proximal ρ-admissible sets. As a companion result, we establish a best proximity pair theorem for pointwise noncyclic contractions in modular spaces. To that end, we provide some examples throughout the paper to illustrate the validity of the obtained results.