Fixed point theorems for simulation functions in b-metric spaces via the wt-distance

Chirasak Mongkolkeha, Yeol Je Cho, Poom Kumam
DOI: https://doi.org/10.4995/agt.2017.6322

Abstract

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. [12]. Also, we give some examples to illustrate our main results.

Keywords

Fixed point; simulation function; b-metric space; wt-distance; w-distance; generalized distance

Subject classification

47H09; 47H10; 54H25

Full Text:

PDF

References

A. N. Abdou, Y. J. Cho and R. Saadati, Distance type and common fixed point theorems in Menger probabilistic metric type spaces, Appl. Math. Comput. 265 (2015), 1145-1154. 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), 381--391.

F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat 96 (2015), 1189-1194. 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 simulation function, J. Comput. Appl. Math. 275 (2015), 345-355. 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, 1989, Pitman Res. Notes Math. Ser. 252: Longman Sci. Tech., Harlow, 1991, pp. 39-406.

W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and its Applications, Yokohama Publishers, Yokahama, Japan, 2000.

Abstract Views

3652
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share


Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt