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

Ei Ei Nyein, Aung Khaing Zaw

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.

Keywords


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

Full Text:

PDF

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.




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

Refbacks




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