On multivalued maps for φ-contractions involving orbits with application

Ali A., Arshad M., Asif A., Savas E., Park C., Shin D. Y.

AIMS Mathematics, cilt.6, sa.7, ss.7532-7554, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 7
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3934/math.2021440
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.7532-7554
  • Anahtar Kelimeler: B-Bianchini-Grandolfi gauge function, B-metric space, Fixed point, Simulation function
  • Uşak Üniversitesi Adresli: Hayır

Özet

In [14], Proinov established the existence of fixed point theorems regarding as a generalization of the Banach contraction principle (BCP) of self mapping under an influence of gauge function (GF). In this paper, we develop some existence results on φ-contraction for multivalued maps via b-Bianchini-Grandolfi gauge function (B-GGF) in class of b-metric spaces and consequently assure the existence results in the module of simulation function as well α-admissible mapping. An extensive set of nontrivial example is given to justify our claim. At the end, we give an application to prove the existence behavior for the system of integral inclusion.