Geodesic
Fixed point results for generalized multi-valued contractions
Ahmad, Jamshaid1 ; Hussain, Nawab2 ; Khan, Abdul Rahim3 ; Azam, Akbar1
1 Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 909-918.

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

Javahernia et al. [Fixed Point Theory and Applications 2014, 2014:195] introduced the concept of generalized Mizoguchi-Takahashi type contractions and established some common fixed point results for such contractions. In this paper, we define the notion of generalized $\alpha_*$ Mizoguchi-Takahashi type contractions and obtain some new fixed point results which generalize various results existing in literature. An example is included to show that our results are genuine generalization of the corresponding known results.
DOI : 10.22436/jnsa.008.06.02
Classification : 47H10, 54H25
Keywords: Metric space, fixed point, MT-function

Ahmad, Jamshaid 1 ; Hussain, Nawab 2 ; Khan, Abdul Rahim 3 ; Azam, Akbar 1

1 Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 
@article{JNSA_2015_8_6_a1,
     author = {Ahmad, Jamshaid and Hussain, Nawab and Khan, Abdul Rahim and Azam, Akbar},
     title = {Fixed point results for generalized multi-valued contractions},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {909-918},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {2015},
     doi = {10.22436/jnsa.008.06.02},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.02/}
}
TY  - JOUR
AU  - Ahmad, Jamshaid
AU  - Hussain, Nawab
AU  - Khan, Abdul Rahim
AU  - Azam, Akbar
TI  - Fixed point results for generalized multi-valued contractions
JO  - Journal of nonlinear sciences and its applications
PY  - 2015
SP  - 909
EP  - 918
VL  - 8
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.02/
DO  - 10.22436/jnsa.008.06.02
LA  - en
ID  - JNSA_2015_8_6_a1
ER  - 
%0 Journal Article
%A Ahmad, Jamshaid
%A Hussain, Nawab
%A Khan, Abdul Rahim
%A Azam, Akbar
%T Fixed point results for generalized multi-valued contractions
%J Journal of nonlinear sciences and its applications
%D 2015
%P 909-918
%V 8
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.02/
%R 10.22436/jnsa.008.06.02
%G en
%F JNSA_2015_8_6_a1
Ahmad, Jamshaid; Hussain, Nawab; Khan, Abdul Rahim; Azam, Akbar. Fixed point results for generalized multi-valued contractions. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 909-918. doi : 10.22436/jnsa.008.06.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.02/

[1] Ahmad, J.; Al-Rawashdeh, A.; A. Azam Fixed point results for \(\{\alpha,\xi\}\)-expansive locally contractive mappings, J. Inequal. Appl., Volume 2014 (2014), pp. 1-10

[2] Asl, J. H.; Rezapour, S.; Shahzad, N. On fixed points of \(\alpha-\psi\) contractive multifunctions, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-6

[3] Azam, A.; M. Arshad Fixed points of a sequence of locally contractive multivalued maps , Comp. Math. Appl., Volume 57 (2009), pp. 96-100

[4] Banach, S. Sur les opérations dans les ensembles abstraits et leur application aux equations itegrales , Fund. Math. , Volume 3 (1922), pp. 133-181

[5] Ćirić, L.; Abbas, M.; Saadati, R.; Hussain, N. Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., Volume 217 (2011), pp. 5784-5789

[6] Hussain, N.; Salimi, P.; Latif, A. Fixed point results for single and set-valued \(\alpha-\eta-\psi\)-contractive mappings, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-23

[7] Hussain, N.; Ahmad, J.; Azam, A. Generalized fixed point theorems for multivalued \(\alpha-\psi\)-contractive mappings , J. Ineq. Appl., Volume 2014 (2014), pp. 1-15

[8] Hussain, N.; Yasmin, N.; Shafqat, N. Multi-valued Ćirić contractions on metric spaces with applications, Filomat, Volume 28 (2014), pp. 1953-1964

[9] Hussain, N.; Parvaneh, V.; Ghoncheh, S. J. Hoseini Generalized contractive mappings and weakly \(\alpha\)-admissible pairs in G-metric spaces, The Scientific World J., Volume 2014 (2014), pp. 1-15

[10] Javahernia, M.; Razani, A.; Khojasteh, F. Common fixed point of the generalized Mizoguchi-Takahashi's type contractions, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-12

[11] Kadelburg, Z.; Kumam, P.; Radenović, S.; Sintunavarat, W. Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property, Fixed Point Theory Appl., Volume 2015 (2015), pp. 1-14

[12] Kamran, T. Mizoguchi-Takahashi's type fixed point theorem, Comp. Math. Appl., Volume 57 (2009), pp. 507-511

[13] Kiran, Q.; Ali, M. U.; Kamran, T. Generalization of Mizoguchi-Takahashi type contraction and related fixed point theorems, J. Ineq. Appl., Volume 2014 (2014), pp. 1-9

[14] Kutbi, M. A.; Ahmad, J.; A. Azam On fixed points of \(\alpha-\psi\)- contractive multi- valued mappings in cone metric spaces, Abst. Appl. Anal., Volume 2013 (2013), pp. 1-6

[15] Mizoguchi, N.; W. Takahashi Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., Volume 141 (1989), pp. 177-188

[16] Nadler, Jr. Multivalued contraction mappings, Pacific J. Math., Volume 30 (1969), pp. 195-208

[17] Nashine, H.; Golubović, Z.; Kadelburg, Z. Modified \(\psi\)-contractive mappings in ordered metric spaces and applications, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-18

[18] Reich, S. Fixed points of contractive functions, Boll. Unione Mat. Ital., Volume 5 (1972), pp. 26-42

[19] Salimi, P.; Latif, A.; Hussain, N. Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-19

[20] Takahashi, W. Nonlinear Functional Analysis, Fixed Point Theory Appl., Yokohama Publishers, Yokohama, 2000

Cité par Sources :