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

Chirasak Mongkolkeha, Yeol Je Cho, Poom Kumam


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.


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

Subject classification

47H09; 47H10; 54H25.

Full Text:



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.

A. D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc. 131 (2003), 3647-3656.

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.

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.

J. Heinonen, Lectures on Analysis on Metric Spaces, Springer, Berlin, 2001.

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.

M. Imdad and F. Rouzkard, Fixed point theorems in ordered metric spaces via w-distances, Fixed Point Theory Appl. (2012), 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.

B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-90.

B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683-2693.

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.

N. Shioji, T. Suzuki and W. Takahashi Contractive mappings, Kanan mapping and metric completeness, Proc. Amer. Math. Soc. 126 (1998), 3117-3124.

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.

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