Fixed point theorems for simulation functions in $\mbox{b}$-metric spaces via the $wt$-distance

• Autores: Chirasak Mongkolkeha, Yeol Je Cho, Poom Kumam
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 1, 2017, págs. 91-105
• Idioma: inglés
• DOI: 10.4995/agt.2017.6322
• Enlaces
  • Texto completo
• Resumen

  • The purpose of this article is to prove some fixed point theorems for simulation functions  in complete b-metric   spaces with partially ordered  by using wt-distance which introduced by   Hussain et al.  Also, we give some  examples to illustrate  our  main results.

• Referencias bibliográficas
  • A. N. Abdou, Y. J. Cho and R. Saadati, Distance type and common fixed point theorems in Menger probabilistic metric type spaces, Appl. Math....
  • https://doi.org/10.1016/j.amc.2015.05.052
  • A. D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc. 131 (2003), 3647-3656.
  • https://doi.org/10.1090/S0002-9939-03-06937-5
  • A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
  • S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math. 3 (1922), 133-181.
  • V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, 1993, 3-9.
  • V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum. 9 (2004), 43-53.
  • L. B. Ciric, A generalization of Banach principle, Proc. Amer. Math. Soc. 45 (1974), 267-273.
  • https://doi.org/10.2307/2040075
  • S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
  • S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena 46 (1998), 263-276.
  • M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604-608.
  • https://doi.org/10.1090/S0002-9939-1973-0334176-5
  • J. Heinonen, Lectures on Analysis on Metric Spaces, Springer, Berlin, 2001.
  • https://doi.org/10.1007/978-1-4613-0131-8
  • N. Hussain, R. Saadati and R. P. Agrawal, On the topology and wt-distance on metric type spaces, Fixed Point Theory Appl. (2014), 2014:88.
  • https://doi.org/10.1186/1687-1812-2014-88
  • M. Imdad and F. Rouzkard, Fixed point theorems in ordered metric spaces via w-distances, Fixed Point Theory Appl. (2012), 2012:222.
  • https://doi.org/10.1186/1687-1812-2012-222
  • O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996),...
  • F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat 96 (2015),...
  • https://doi.org/10.2298/FIL1506189K
  • B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-90.
  • https://doi.org/10.1090/S0002-9947-1977-0433430-4
  • B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683-2693.
  • https://doi.org/10.1016/S0362-546X(01)00388-1
  • A. Roldán-Lopez-de-Hierro, E. Karapinar, C. Roldán-Lopez-de-Hierro and J. Martinez-Morenoa, Coincidence point theorems on metric spaces via...
  • https://doi.org/10.1016/j.cam.2014.07.011
  • N. Shioji, T. Suzuki and W. Takahashi Contractive mappings, Kanan mapping and metric completeness, Proc. Amer. Math. Soc. 126 (1998), 3117-3124.
  • https://doi.org/10.1090/S0002-9939-98-04605-X
  • W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, in Fixed Point Theory and Applications, Marseille,...
  • W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and its Applications, Yokohama Publishers, Yokahama, Japan, 2000.