P-CONTRACTIVE MAPPINGS ON METRIC SPACES

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ALTUN İ., DURMAZ G., OLGUN M.

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, cilt.2018, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2018
  • Basım Tarihi: 2018
  • Doi Numarası: 10.23952/jnfa.2018.43
  • Dergi Adı: JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: Contractive mapping, P-contractive mapping, Fixed point, Compact metric space, FIXED-POINT THEOREMS
  • Ankara Üniversitesi Adresli: Evet

Özet

In the present paper, we introduce a new concept of P-contractive mappings on metric spaces. We prove that every ordinary contractive mapping is also P-contractive but the converse may not be true in general. We provide an example to illustrate this fact and also provide some examples to show that nonexpensive mappings and P-contractive mappings are independent on metric spaces. Finally, we present that every continuous P-contractive mapping on compact metric spaces has a unique fixed point. This result includes the famous Edelstein fixed point theorem.