Best Proximity Theory in Metrically Convex Menger PM-Spaces via Cyclic Kannan Maps

Gabeleh M., UYANIK EKİCİ E., Aphane M.

Symmetry, cilt.17, sa.9, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 9
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17091549
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: best proximity point, cyclic relatively Kannan nonexpansive mappings, metrically convex Menger PM-space, probabilistic proximal quasi-normal structure, weak cyclic Kannan contractions
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

A Takahashi convex structure is considered on Menger PM-spaces and used to investigate the existence of best proximity points for weak cyclic Kannan contractions. We then introduce a concept of a probabilistic proximal quasi-normal structure on a convex pair of subsets of Menger PM-spaces and prove that every compact and convex pair in metrically convex Menger PM-spaces has the probabilistic proximal quasi-normal structure. By applying this geometric property, we survey the existence of a best proximity point for cyclic relatively Kannan nonexpansive maps which preserves distance. In order to provide more accurate results, we obtain the same conclusions in the framework of CAT (Formula presented.) spaces.