On multi-valued weak quasi-contractions in b-metric spaces
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Zoran D. Mitrović
- Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina.
We introduce some generalizations of the contractions for multi-valued mappings and establish some fixed point theorems
for multi-valued mappings in b-metric spaces. Our results generalize and extend several known results in b-metric and metric
spaces. Some examples are included which illustrate the cases when the new results can be applied while the old ones cannot.
Share and Cite
Nawab Hussain, Zoran D. Mitrović, On multi-valued weak quasi-contractions in b-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3815--3823
Hussain Nawab, Mitrović Zoran D., On multi-valued weak quasi-contractions in b-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(7):3815--3823
Hussain, Nawab, Mitrović, Zoran D.. "On multi-valued weak quasi-contractions in b-metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3815--3823
- Fixed points
- b-metric space
- set-valued mapping.
M. Abbas, N. Hussain, B. E. Rhoades, Coincidence point theorems for multivalued f-weak contraction mappings and applications, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 105 (2011), 261–272.
A. Amini-Harandi, Fixed point theory for set-valued quasi-contraction maps in metric spaces, Appl. Math. Lett., 24 (2011), 1791–1794.
H. Aydi, M. F. Bota, E. Karapınar, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 8 pages.
I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, 30 (1989), 26–37.
M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326 (2007), 772–782.
S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727–730.
L. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd) (N.S.), 12 (1971), 19–26.
L. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267–273.
M. Cosentino, P. Salimi, P. Vetro, Fixed point results on metric-type spaces, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1237–1253.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 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.
N. Hussain, A. Amini-Harandi, J. Y. Cho, Approximate endpoints for set-valued contractions in metric spaces, Fixed Point Theory Appl., 2010 (2010), 13 pages.
N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 12 pages.
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly \(( \psi,\varphi, L,A, B)\)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013 (2013), 18 pages.
N. Hussain, R. Saadati, R. P. Agrawal, On the topology and wt-distance on metric type spaces, Fixed Point Theory Appl., 2014 (2014), 14 pages.
N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677–1684.
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71–76.
M. A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., 2010 (2010), 7 pages.
M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123–3129.
R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl., 19 (2017), 2153–2163
S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–488.
S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121–124.
J. R. Roshan, V. Parvaneh, I. Altun, Some coincidence point results in ordered b-metric spaces and applications in a system of integral equations, Appl. Math. Comput., 226 (2014), 725–737.
J. R. Roshan, V. Parvaneh, S. Radenović, M Rajović, Some coincidence point results for generalized (\(\psi,\varphi\))-weakly contractions in ordered b-metric spaces, Fixed Point Theory Appl., 2015 (2015), 21 pages.
J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei,W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)- contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages.
S. Shukla, S. Radenović, C. Vetro, Set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces, Int. J. Math. Math. Sci., 2014 (2014), 9 pages.