Geodesic
Geraghty and Ćirić type fixed point theorems in b-metric spaces
Pant, Rajendra1 ; Panicker, R.2
1 Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India
2 Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 11, p. 5741-5755.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we obtain some بهxed point theorems for admissible mappings in b-metric spaces. Some useful examples are given to illustrate the facts. We also discuss an application to a nonlinear quadratic integral equation. Our results complement, extend and generalize a number of بهxed point theorems including the well-known Geraghty [M. A. Geraghty, Proc. Amer. Math. Soc., 40 (1973), 604-608] and Ćirić[L. B. Ćirić, Proc. Amer. Math. Soc., 45 (1974), 267-273] theorems on b-metric spaces.
DOI : 10.22436/jnsa.009.11.03
Classification : 47H10, 54H25
Keywords: Fixed point, b-metric spaces, generalized \(\alpha\)-quasi-contraction, (\(\alpha،\beta\))- Geraghty type contractive mapping

Pant, Rajendra 1 ; Panicker, R. 2

1 Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India
2 Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa 
@article{JNSA_2016_9_11_a2,
     author = {Pant, Rajendra and Panicker, R.},
     title = {Geraghty and {\'Ciri\'c} type fixed point theorems in b-metric spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {5741-5755},
     publisher = {mathdoc},
     volume = {9},
     number = {11},
     year = {2016},
     doi = {10.22436/jnsa.009.11.03},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.03/}
}
TY  - JOUR
AU  - Pant, Rajendra
AU  - Panicker, R.
TI  - Geraghty and Ćirić type fixed point theorems in b-metric spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2016
SP  - 5741
EP  - 5755
VL  - 9
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.03/
DO  - 10.22436/jnsa.009.11.03
LA  - en
ID  - JNSA_2016_9_11_a2
ER  - 
%0 Journal Article
%A Pant, Rajendra
%A Panicker, R.
%T Geraghty and Ćirić type fixed point theorems in b-metric spaces
%J Journal of nonlinear sciences and its applications
%D 2016
%P 5741-5755
%V 9
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.03/
%R 10.22436/jnsa.009.11.03
%G en
%F JNSA_2016_9_11_a2
Pant, Rajendra; Panicker, R. Geraghty and Ćirić type fixed point theorems in b-metric spaces. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 11, p. 5741-5755. doi : 10.22436/jnsa.009.11.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.03/

[1] Aghajani, A.; Abbas, M.; Roshan, J. R. Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, Volume 64 (2014), pp. 941-960

[2] Alizadeh, S.; Moradlou, F.; Salimi, P. Some fixed point results for \((\alpha,\beta)-(\psi,\phi)\)-contractive mappings, Filomat, Volume 28 (2014), pp. 635-647

[3] Allahyari, R.; Arab, R.; Haghighi, A. Shole Fixed points of admissible almost contractive type mappings on b-metric spaces with an application to quadratic integral equations, J. Inequal. Appl., Volume 2015 (2015), pp. 1-18

[4] An, T. V.; Tuyen, L. Q.; Dung, N. V. Stone-type theorem on b-metric spaces and applications, Topology Appl., Volume 185/186 (2015), pp. 50-64

[5] Boriceanu, M.; Bota, M.; Petruşel, A. Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., Volume 8 (2010), pp. 367-377

[6] Boriceanu, M.; Petruşel, A.; Rus, I. A. Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat., Volume 6 (2010), pp. 65-76

[7] Chandok, S. Some fixed point theorems for (\(\alpha,\beta\))-admissible Geraghty type contractive mappings and related results, Math. Sci. (Springer), Volume 9 (2015), pp. 127-135

[8] Cho, S.-H.; Bae, J.-S. Fixed points of weak \(\alpha\)-contraction type maps, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-12

[9] Ćirić, L. B. A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., Volume 45 (1974), pp. 267-273

[10] Czerwik, S. Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, Volume 1 (1993), pp. 5-11

[11] Czerwik, S. Nonlinear set-valued contraction mappings in b-metric spaces, Atti. Sem. Mat. Fis. Univ. Modena, Volume 46 (1998), pp. 263-276

[12] Czerwik, S.; Dlutek, K.; Singh, S. L. Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci., Volume 11 (1997), pp. 87-94

[13] Geraghty, M. A. On contractive mappings, Proc. Amer. Math. Soc., Volume 40 (1973), pp. 604-608

[14] Karapınar, E.; Kumam, P.; Salimi, P. On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-12

[15] Karapınar, E.; Samet, B. Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., Volume 2012 (2012), pp. 1-17

[16] Kumam, P.; Dung, N. V.; Sitthithakerngkiet, K. A generalization of Ćirić fixed point theorems, Filomat, Volume 29 (2015), pp. 1549-1556

[17] Latif, A.; Parvaneh, V.; Salimi, P.; Al-Mazrooei, A. E. Various Suzuki type theorems in b-metric spaces, J. Nonlinear Sci. Appl., Volume 8 (2015), pp. 363-377

[18] Rhoades, B. E. A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., Volume 226 (1977), pp. 257-290

[19] Samet, B.; Vetro, C.; Vetro, P. Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., Volume 75 (2012), pp. 2154-2165

[20] Singh, S. L.; Bhatnagar, C.; Mishra, S. N. Stability of iterative procedures for multivalued maps in metric spaces, Demonstratio Math., Volume 37 (2005), pp. 905-916

[21] Sintunavarat, W.; Plubtieng, S.; Katchang, P. Fixed point result and applications on a b-metric space endowed with an arbitrary binary relation, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-13

Cité par Sources :