Quasi (s,r)-Contractive Multi-Valued Operators on b-Metric Space and Related Fixed Point Theorems

Ei Ei Nyein, Aung Khaing Zaw


This paper aims to introduce a new type of quasi (s,r)-contractive multi-valued operator on b-complete metric space and to extend the results for the fixed point theorems of quasi (s,r)-contractive multi-valued operator. As an application, the  existence of the solution for a type of differential equation is given.


b-metric space; quasi (s,r)-contractive multi-valued operator; fixed point theorem.

Full Text:



S.L. Singh, S. Czerwik, K. Kr ol, A. Singh,, Coincidences and fixed points of hybrid contractions, Tamsui Oxf. J. Math. Sci., 24, (2008), 401416.

S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1, (1993), 5-11.

S. Czerwick, Nonlinear set-valued contraction mappings in b-metric spaces, Atti del Seminario Matematico e Fisico dellUniversit‘a di Modena, 46, (1998), 263276.

Ei Ei Nyein, Dianlu Tian, Aung Khaing Zaw, Quasi (s,r)-Contractive Multi-Valued Operators and Related Fixed Point Theorems, Mathematics, 2020, 8(1), 64; doi:10.3390/math8010064.

M. Jleli, B. Samet, C. Vetro, F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstract and Applied Analysis, 2015 (2015), 1-7.

William Kirk, Naseer Shahzad, Fixed Point Theory in Distance Spaces, Springer, New York, (2014).

Radu Miculescu, Alexandru Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, arXiv:1512.03967v1 [math.CA] 12, Dec (2015).

H. Aydi, M.F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory and Applications, 2012, (2012): 88.

L.B. Ciric, A generalization of Banachs contraction principle, Proc. Amer. Math. Soc., 45 (2) (1974), 267273.

S.B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475488.

O. Popescu, A new type of contractive multivalued operators, Bull. Sci. Math., 137, (2013), 30-44.

A. Amini-Harandi, Fixed point theory for set-valued quasi-contraction maps in metric spaces, Appl. Math. Lett., 24, (2011), 1791-1794.

R.H. Haghi,S. Rezapour, N. Shahzad, On fixed points of quasi-contraction type multifunctions, Appl. Math. Lett., 25, (2012), 843-846.

Lingjuan Ye, Congcong Shen, weakly (s,r)-contractive multi-valued operators on b-mettric space, J.Nonlinear Sci. Appl., 11 (2018), 358-367.

J.R. Roshan, V. Parvaneh, Z. Kadelburg, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229245.

M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377.

DOI: https://doi.org/10.22342/jims.26.3.941.393-402


Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats