EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES

Title & Authors
EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES
Afshari, Hojjat; Aydi, Hassen; Karapinar, Erdal;

Abstract
In this paper, we introduce the notion of generalized $\small{{\alpha}-{\psi}}$-Geraghty multivalued mappings and investigate the existence of a xed point of such multivalued mappings. We present a concrete example and an application on integral equations illustrating the obtained results.
Keywords
b-metric space;generalized $\small{{\alpha}-{\psi}}$-Geraghty multivalued mappings;fixed point;
Language
English
Cited by
References
1.
A. Felhi, S. Sahmim, and H. Aydi, Ulam-Hyers stability and well-posedness of fixed point problems for $\alpha$- $\lambda$-contractions on quasi b-metric spaces, Fixed Point Theory Appl. (2016), 2016:1.

2.
M. U. Ali, T. Kamran, and E. Karapinar, On ($\alpha$, $\psi$, $\eta$)-contractive multivalued mappings, Fixed Point Theory Appl. (2014), 2014:7.

3.
H. Aydi, M.F. Bota, E. Karapinar, and S. Moradi, A common fixed point for weak $\phi$-contractions on b-metric spaces, Fixed Point Theory, 13 (2012), no. 2, 337-346.

4.
H. Aydi, E. Karapinar, M.F. Bota, and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012:88.

5.
H. Aydi, A. Felhi, and S. Sahmim, Common fixed points in rectangular b-metric spaces using (E:A) property, Journal of Advanced Mathematical Studies, 8 (2015), no. 2, 159-169.

6.
H. Aydi, M. Jellali, and E. Karapinar, Common fixed points for generalized $\alpha$-implicit contractions in partial metric spaces: Consequences and application, RACSAM, 109 (2015), no. 2, 367-384.

7.
H. Aydi, M. Jellali, and E. Karapinar, On fixed point results for $\alpha$-implicit contractions in quasi-metric spaces and consequences, Nonlinear Analysis: Modelling and Control, 21 (2016), no. 1, 40-56.

8.
H. Aydi, E. Karapinar, and B. Samet, Fixed points for generalized ($\alpha$, $\psi$)-contractions on generalized metric spaces, Journal Ineq. Appl. (2014), 2014:229.

9.
A. Azam, N. Mehmood, J. Ahmad, and S. Radenovic, Multivalued fixed point theorems in cone b-metric spaces, Journal Ineq. Appl. 2013, 2013:582.

10.
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena. 46 (1998), no. 2, 263-276.

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

12.
M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604-?08.

13.
M. Jleli, B. Samet, C. Vetro, and F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstract and Applied Analysis, Volume 2015, Article ID 718074, 7 pages.

14.
M. Jovanovic, Z. Kadelburg, and S. Radenovic, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. Volume 2010, Article ID 978121, 15 pages.

15.
H. Huang, and S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl. (2013), 2013:112.

16.
N. Hussian, and M.H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011), 1677-1684.

17.
E. Karapinar, and B. Samet, Generalized $\alpha$-$\psi$-contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, Volume 2012 (2012), Article ID 793486, 17 pages.

18.
E. Karapinar, Fixed point theorems on $\alpha$-$\psi$-Geraghty contraction type mappings, Filomat (2014), 761-766.

19.
E. Karapinar, $\alpha$-$\psi$-Geraghty contraction type mappings and some related fixed point results, Filomat (2014), 37-48.

20.
E. Karapinar, P. Kumam, and P. Salimi, On $\alpha$-$\psi$-Meir-Keeler contractive mappings, Fixed Point Theory Appl. (2013), 2013:94.

21.
B. Mohammadi, Sh. Rezapour, and N.Shahzad Some results of fixed point of $\alpha$-$\psi$-quasi-contractive multifunctions, Fixed Point Theory Appl. (2013), 2013:112.

22.
B. Mohammadi, S Rezapour, and N Shahzad, Some results on fixed points of $\alpha$-$\psi$-Ciric generalized multifunctions, Fixed Point Theory Appl. (2013), 2013:24.

23.
O. Popescu, Some new fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. (2014), 2014:190

24.
J.R. Roshan, V. Parvaneh, Sh. Sedghi, N. Shobkolaei, and W. Shatanawi, Common fixed points of almost generalized $({\psi}-{\varphi})_s$-contraction mappings in ordered b-metric spaces. Fixed Point Theory Appl. (2013), 2013:159.

25.
B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for $\alpha$-$\psi$-contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.

26.
R.J. Shahkoohi, and A. Razani, Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, Journal Ineq. Appl. (2014), 2014:373.

27.
L. Shi, and S. Xu, Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces, Fixed Point Theory Appl. (2013), 2013:120.