phi-Best proximity point theorems and applications to variational inequality problems

Isik H., Sezen M., Vetro C.

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, cilt.19, sa.4, ss.3177-3189, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s11784-017-0479-0
  • Dergi Adı: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3177-3189
  • Anahtar Kelimeler: (F, phi)-proximal contraction, (F, phi)-weak proximal contraction, phi-best proximity point, partial metric space, metric projection, variational inequality, PARTIAL METRIC-SPACES, EXISTENCE, CONVERGENCE
  • Gazi Üniversitesi Adresli: Hayır

Özet

The main concern of this study is to introduce the notion of -best proximity points and establish the existence and uniqueness of -best proximity point for non-self mappings satisfying -proximal and -weak proximal contraction conditions in the context of complete metric spaces. Some examples are supplied to support the usability of our results. As applications of the obtained results, some new best proximity point results in partial metric spaces are presented. Furthermore, sufficient conditions to ensure the existence of a unique solution for a variational inequality problem are also discussed.