A Note on farthest point problem in banach spaces

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Som S., SAVAŞ E.

Miskolc Mathematical Notes, cilt.20, sa.2, ss.1237-1243, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18514/mmn.2019.2834
  • Dergi Adı: Miskolc Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1237-1243
  • Anahtar Kelimeler: Farthest point map, Ideal, Partial ideal statistical continuity, Uniquely remotal
  • Uşak Üniversitesi Adresli: Evet

Özet

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F: X→E restricted to [c,F(c)] is partially ideal statistically continuous at c then E is singleton.