ON A NEW CLASS OF MULTIVALUED WEAKLY PICARD OPERATORS ON COMPLETE METRIC SPACES

ALTUN İ., OLGUN M., Minak G.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.19, sa.3, ss.659-672, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 3
  • Basım Tarihi: 2015
  • Doi Numarası: 10.11650/tjm.19.2015.4752
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.659-672
  • Anahtar Kelimeler: Weakly Picard operator, Fixed point, Multivalued mappings, Nonlinear F-contractions, Complete metric space, FIXED-POINT THEOREMS, CONTRACTION-MAPPINGS
  • Ankara Üniversitesi Adresli: Evet

Özet

In the present paper, the concept of nonlinear F-contraction for multivalued mappings in metric spaces is introduced and considering the new proof technique, which was used for single valued maps by Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 2012: 94, 6 pp.], we demonstrate that multivalued nonlinear F-contractions of Ciric type are weakly Picard operators on complete metric spaces. Finally, we give a nontrivial example to guarantee that our result is veritable generalization of recent result of Ciric [Lj. B. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Analysis, 71 (2009), 2716-2723]. Also, we show that many fixed point results in the literature can not be applied to this example.