Geodesic
Generalized Suzuki type $ \alpha $-$ \mathcal{Z} $-contraction in b-metric space
Antal, Swati1 ; Gairola, U. C. 1
1 Department of Mathematics, H.N.B. Garhwal University, BGR Campus, Pauri Garhwal-246001, Uttarakhand, India
Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 4, p. 212-222.

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

In this paper, we introduce the concept of generalized Suzuki type $\alpha$-$ \mathcal{Z} $-contraction concerning a simulation function $\zeta$ in b-metric space and prove the existence of fixed point results for this contraction. Our result extend the fixed point result of [A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya, Kragujevac J. Math., $\bf 42$ (2018), 419--430].
DOI : 10.22436/jnsa.013.04.06
Classification : 54H25, 47H10
Keywords: Simulation function, triangular \(\alpha\)-admissible mapping with respect to \(\zeta\) \sep b-metric space, generalized Suzuki type \(\alpha\)-\( \mathcal{Z} \)-contraction mapping

Antal, Swati 1 ; Gairola, U. C.  1

1 Department of Mathematics, H.N.B. Garhwal University, BGR Campus, Pauri Garhwal-246001, Uttarakhand, India 
@article{JNSA_2020_13_4_a5,
     author = {Antal, Swati and Gairola, U. C. },
     title = {Generalized {Suzuki} type \( \alpha \)-\( {\mathcal{Z}} \)-contraction in b-metric space},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {212-222},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2020},
     doi = {10.22436/jnsa.013.04.06},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.04.06/}
}
TY  - JOUR
AU  - Antal, Swati
AU  - Gairola, U. C. 
TI  - Generalized Suzuki type \( \alpha \)-\( \mathcal{Z} \)-contraction in b-metric space
JO  - Journal of nonlinear sciences and its applications
PY  - 2020
SP  - 212
EP  - 222
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.04.06/
DO  - 10.22436/jnsa.013.04.06
LA  - en
ID  - JNSA_2020_13_4_a5
ER  - 
%0 Journal Article
%A Antal, Swati
%A Gairola, U. C. 
%T Generalized Suzuki type \( \alpha \)-\( \mathcal{Z} \)-contraction in b-metric space
%J Journal of nonlinear sciences and its applications
%D 2020
%P 212-222
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.04.06/
%R 10.22436/jnsa.013.04.06
%G en
%F JNSA_2020_13_4_a5
Antal, Swati; Gairola, U. C. . Generalized Suzuki type \( \alpha \)-\( \mathcal{Z} \)-contraction in b-metric space. Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 4, p. 212-222. doi : 10.22436/jnsa.013.04.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.04.06/

[1] Aydi, H.; Jellali, M.; Karapinar, E. On fixed point results for $\alpha$-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, Volume 21 (2016), pp. 40-56 | DOI | Zbl

[2] Babu, G. V. R.; Mosissa, D. T. Fixed point in $b$-metric space via simulation function, Novi Sad J. Math., Volume 47 (2017), pp. 133-147

[3] Boriceanu, M. Strict fixed point theorems for multivalued operators in $b$-metric space, Int. J. Mod. Math., Volume 4 (2009), pp. 285-301

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

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

[6] Demma, M.; Saadati, R.; Vetro, P. Fixed point results on $b$-metric space via Picard sequences and $b$-simulation functions, Iran. J. Math. Sci. Inform., Volume 11 (2016), pp. 123-136 | DOI | Zbl

[7] Karapinar, E.; Kumam, P.; Salimi, P. On $\alpha$-$\psi$-Meir-Keeler contractive mappings, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-12 | Zbl | DOI

[8] Khojasteh, F.; Shukla, S.; Radenović, S. A new approach to the study of fixed point theory for simulation functions, Filomat, Volume 29 (2015), pp. 1189-1194 | Zbl

[9] Kumam, P.; Gopal, D.; Budhia, L. A new fixed point theorem under Suzuki type $Z$-contraction mappings, J. Math. Anal., Volume 8 (2017), pp. 113-119

[10] Mohammadi, B.; Rezapour, S.; Shahzad, N. Some results on fixed points of $\alpha$-$\psi$-Ciric generalized multifunctions, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-10 | DOI

[11] Pacurar, M. Sequences of almost contractions and fixed points in $b$-metric spaces, An. Univ. Vest Timiş. Ser. Mat.-Inform., Volume 48 (2010), pp. 125-137

[12] Padcharoen, A.; Kumam, P.; Saipara, P.; Chaipunya, P. Generalized Suzuki type $\mathcal{Z}$-contraction in complete metric spaces, Kragujevac J. Math., Volume 42 (2018), pp. 419-430

[13] Roshan, J. R.; Parvaneh, V.; Kadelberg, Z. Common fixed point theorems for weakly isotone increasing mappings in ordered $b$-metric spaces, J. Nonlinear Sci. Appl., Volume 7 (2014), pp. 229-245 | DOI | Zbl

[14] Roshan, J. R.; Parvaneh, V.; Sedghi, S.; Shobkolaei, N.; Shatanawi, W. Common fixed points of almost generalized $(\psi, \phi){s}$-contractive mappings in ordered $b$-metric spaces, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-23 | DOI

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

Cité par Sources :