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

Ei Ei Nyein; Aung Khaing Zaw

doi:10.22342/jims.26.3.941.393-402

Ei Ei Nyein ⁽¹⁾ , Aung Khaing Zaw ⁽²⁾

(1) Beijing Institute of Technology, China,

(2) Beijing Institute of Technology, China

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

Issue
VOLUME 26 NUMBER 3 (NOVEMBER 2020)

Submitted
June 18, 2020

Accepted
September 3, 2020

Published
November 5, 2020

Keywords:

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

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Abstract

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.

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References

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.

Authors

Ei Ei Nyein

Beijing Institute of Technology

Aung Khaing Zaw

Beijing Institute of Technology

akzbee451986@yahoo.com (Primary Contact)

Author Biographies

Ei Ei Nyein, Beijing Institute of Technology

School of Mathematics and Statistics

Aung Khaing Zaw, Beijing Institute of Technology

School of Mathematics and Statistics,

Student

Nyein, E. E., & Khaing Zaw, A. (2020). Quasi (s,r)-Contractive Multi-Valued Operators on b-Metric Space and Related Fixed Point Theorems. Journal of the Indonesian Mathematical Society, 26(3), 393–402. https://doi.org/10.22342/jims.26.3.941.393-402