GENERALIZED -GERAGHTY MULTIVALUED MAPPINGS ON b-METRIC SPACES ENDOWED WITH A GRAPH
Yıl 2017,
Cilt: 7 Sayı: 2, 248 - 260, 01.12.2017
H. Afshari
M. Atapour
H. Aydi
Öz
In this paper, we provide some conditions for the existence of a coincidence point of single-valued and multivalued mappings involving generalized -Geraghty contractions endowed with a graph. Our main results improve the existing results in the corresponding literature. We also present examples to support the obtained results.
Kaynakça
- Afshari,H., Aydi,H., and Karapinar,E., (2016), Some fixed point results for multivalued mappings in b-metric spaces, East Asian Mathematical Journal, Vol.32, No. 3, pp.319-332.
- Aydi,H., Karapinar,E, Bota,M.F., and Mitrovi´c,S., (2012), A fixed point theorem for set-valued quasi- contractions in b-metric spaces, Fixed Point Theory Appl., 2012:88.
- Aydi,H., Felhi,A., and Sahmim,S., (2016), On common fixed points for (α, ψ)-contractions and general- ized cyclic contractions in b-metric-like spaces and consequences, J. Nonlinear Sci. Appl. 9, 2492-2510.
- Aydi,H., Felhi,A., and Sahmim,S., (2015), Common fixed points in rectangular b-metric spaces using
- (E.A) property, Journal of Advanced Mathematical Studies, bf 8 (2) , pp.159-169. Azam,A., Mehmood,N., Ahmad,J., and Radenovi´c,S., (2013), Multivalued fixed point theorems in cone b-metric spaces, J. Ineq. Appl., 2013:582.
- Bakhtin,I.A., (1989), The contraction mapping principle in almost metric spaces, Journal of Functional Analysis, 30, PP.26-37.
- Banach,S., (1922), Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3, pp.133-181.
- Czerwik,S., (1998), Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena 46(2), pp.263-276.
- Czerwik,S., (1993), Contraction mappings in b-metric spaces. Acta Math. Inf. Univ. Ostrav. 1, pp.5-11.
- Felhi,A., Sahmim,S., and Aydi,H., (2016), Ulam-Hyers stability and well-posedness of fixed point prob- lems for α − λ-contractions on quasi b-metric spaces, Fixed Point Theory Appl., 2016:1.
- Jachymski,J., (2008), The contraction principle for mappings on a metric space with a graph, Pro- ceedings of the American Mathematical Society, 136, No. 4, pp.1359-1373.
- Karapinar,E. and Samet,B., (2012), Generalized α − ψ-contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, 2012, Article ID 793486, 17 pages.
- Karapinar,E., (2014), Fixed point theorems on α-ψ-Geraghty contraction type mappings, Filomat, pp.761-766.
- Karapinar,E., (2014), α-ψ-Geraghty contraction type mappings and some related fixed point results, Filomat, pp.37-48.
- Popescu,O., (2014), Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014:190
- Tiammee,J. and Suantai,S., (2014), Coincidence point theorems for graph-preserving multivalued map- pings, Fixed Point Theory Appl. 70, 2014:160.
Yıl 2017,
Cilt: 7 Sayı: 2, 248 - 260, 01.12.2017
H. Afshari
M. Atapour
H. Aydi
Kaynakça
- Afshari,H., Aydi,H., and Karapinar,E., (2016), Some fixed point results for multivalued mappings in b-metric spaces, East Asian Mathematical Journal, Vol.32, No. 3, pp.319-332.
- Aydi,H., Karapinar,E, Bota,M.F., and Mitrovi´c,S., (2012), A fixed point theorem for set-valued quasi- contractions in b-metric spaces, Fixed Point Theory Appl., 2012:88.
- Aydi,H., Felhi,A., and Sahmim,S., (2016), On common fixed points for (α, ψ)-contractions and general- ized cyclic contractions in b-metric-like spaces and consequences, J. Nonlinear Sci. Appl. 9, 2492-2510.
- Aydi,H., Felhi,A., and Sahmim,S., (2015), Common fixed points in rectangular b-metric spaces using
- (E.A) property, Journal of Advanced Mathematical Studies, bf 8 (2) , pp.159-169. Azam,A., Mehmood,N., Ahmad,J., and Radenovi´c,S., (2013), Multivalued fixed point theorems in cone b-metric spaces, J. Ineq. Appl., 2013:582.
- Bakhtin,I.A., (1989), The contraction mapping principle in almost metric spaces, Journal of Functional Analysis, 30, PP.26-37.
- Banach,S., (1922), Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3, pp.133-181.
- Czerwik,S., (1998), Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena 46(2), pp.263-276.
- Czerwik,S., (1993), Contraction mappings in b-metric spaces. Acta Math. Inf. Univ. Ostrav. 1, pp.5-11.
- Felhi,A., Sahmim,S., and Aydi,H., (2016), Ulam-Hyers stability and well-posedness of fixed point prob- lems for α − λ-contractions on quasi b-metric spaces, Fixed Point Theory Appl., 2016:1.
- Jachymski,J., (2008), The contraction principle for mappings on a metric space with a graph, Pro- ceedings of the American Mathematical Society, 136, No. 4, pp.1359-1373.
- Karapinar,E. and Samet,B., (2012), Generalized α − ψ-contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, 2012, Article ID 793486, 17 pages.
- Karapinar,E., (2014), Fixed point theorems on α-ψ-Geraghty contraction type mappings, Filomat, pp.761-766.
- Karapinar,E., (2014), α-ψ-Geraghty contraction type mappings and some related fixed point results, Filomat, pp.37-48.
- Popescu,O., (2014), Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014:190
- Tiammee,J. and Suantai,S., (2014), Coincidence point theorems for graph-preserving multivalued map- pings, Fixed Point Theory Appl. 70, 2014:160.