Geodesic
Fixed point results and an application to homotopy in modular metric spaces
Ege, Meltem Erden1 ; Alaca, Cihangir2
1 Department of Mathematics, Institute of Natural and Applied Sciences, Celal Bayar University, Muradiye Campus 45140, Manisa, Turkey
2 Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, 45140 Manisa, Turkey
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 900-908.

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

The purpose of this paper is to define new concepts, such as T-orbitally w-completeness, orbitally w-continuity and almost weakly w-contractive mapping in the modular metric spaces. We prove some fixed point theorems for these related concepts and mappings in this space. Further, we give an application using the technique in [Lj. B. Ćirić, B. Samet, H. Aydi, C. Vetro, Appl. Math. Comput., 218 (2011), 2398-2406] and show that our results can be applied to homotopy.
DOI : 10.22436/jnsa.008.06.01
Classification : 46A80, 47H10, 54E35
Keywords: Modular metric space, T-orbitally w-completeness, orbitally w-continuity, fixed point.

Ege, Meltem Erden 1 ; Alaca, Cihangir 2

1 Department of Mathematics, Institute of Natural and Applied Sciences, Celal Bayar University, Muradiye Campus 45140, Manisa, Turkey
2 Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, 45140 Manisa, Turkey 
@article{JNSA_2015_8_6_a0,
     author = {Ege, Meltem Erden and Alaca, Cihangir},
     title = {Fixed point results and an application to homotopy in modular metric spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {900-908},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {2015},
     doi = {10.22436/jnsa.008.06.01},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.01/}
}
TY  - JOUR
AU  - Ege, Meltem Erden
AU  - Alaca, Cihangir
TI  - Fixed point results and an application to homotopy in modular metric spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2015
SP  - 900
EP  - 908
VL  - 8
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.01/
DO  - 10.22436/jnsa.008.06.01
LA  - en
ID  - JNSA_2015_8_6_a0
ER  - 
%0 Journal Article
%A Ege, Meltem Erden
%A Alaca, Cihangir
%T Fixed point results and an application to homotopy in modular metric spaces
%J Journal of nonlinear sciences and its applications
%D 2015
%P 900-908
%V 8
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.01/
%R 10.22436/jnsa.008.06.01
%G en
%F JNSA_2015_8_6_a0
Ege, Meltem Erden; Alaca, Cihangir. Fixed point results and an application to homotopy in modular metric spaces. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 900-908. doi : 10.22436/jnsa.008.06.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.01/

[1] Alaca, C.; Ege, M. E.; Park, C. Fixed point results for modular ultrametric spaces, preprint , , 2014

[2] Azadifar, B.; Maramaei, M.; Sadeghi, G. Common fixed point theorems in modular G-metric spaces, J. Nonlinear Anal. Appl., Volume 2013 (2013), pp. 1-9

[3] Azadifar, B.; Maramaei, M.; Sadeghi, G. On the modular G-metric spaces and fixed point theorems, J. Nonlinear Sci. Appl., Volume 6 (2013), pp. 293-304

[4] Azadifar, B.; Sadeghi, G.; Saadati, R.; Park, C. Integral type contractions in modular metric spaces, J. Inequal. Appl., Volume 2013 (2013), pp. 1-14

[5] Banach, S. Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., Volume 3 (1922), pp. 133-181

[6] Boyd, D. W.; Wong, J. S. On nonlinear contractions, Proc. Amer. Math. Soc., Volume 20 (1969), pp. 458-464

[7] Chaipunya, P.; Cho, Y. J.; Kumam, P. Geraghty-type theorems in modular metric spaces with an application to partial differential equation, Adv. Difference Equ., Volume 2012 (2012), pp. 1-12

[8] Chistyakov, V. V. Modular metric spaces generated by F-modulars, Folia Math., Volume 15 (2008), pp. 3-24

[9] Chistyakov, V. V. Modular metric spaces I. basic concepts, Nonlinear Anal., Volume 72 (2010), pp. 1-14

[10] Chistyakov, V. V. Fixed points of modular contractive maps, Dokl. Math., Volume 86 (2012), pp. 515-518

[11] Cho, Y. J.; Saadati, R.; G. Sadeghi Quasi-contractive mappings in modular metric spaces, J. Appl. Math., Volume 2012 (2012), pp. 1-5

[12] Ćirić, L. B. On contraction type mapping , Math. Balkanica, Volume 1 (1971), pp. 52-57

[13] Ćirić, L. B. Fixed and periodic points of almost contractive operators, Math. Balkanica, Volume 3 (1973), pp. 33-44

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

[15] Ćirić, L. B.; Samet, B.; Aydi, H.; C. Vetro Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., Volume 218 (2011), pp. 2398-2406

[16] Dehghan, H.; Gordji, M. E.; Ebadian, A. Comment on Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-3

[17] Ege, M. E.; Alaca, C. On Banach fixed point theorem in modular b-metric spaces, preprint , , 2014

[18] Ege, M. E.; Alaca, C. Some properties of modular S-metric spaces and its fixed point results, J. Comput. Anal. Appl., , In Press.

[19] Kilinc, E.; Alaca, C. A fixed point theorem in modular metric spaces, Adv. Fixed Point Theory, Volume 4 (2014), pp. 199-206

[20] Kilinc, E.; Alaca, C. Fixed point results for commuting mappings in modular metric spaces, J. Applied Func. Anal., Volume 10 (2015), pp. 204-210

[21] Mongkolkeha, C.; Sintunavarat, W.; Kumam, P. Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl., Volume 2011 (2011), pp. 1-9

[22] Nakano, H. Modulared semi-ordered linear space, Maruzen Co, Tokyo, 1950

[23] Orlicz, W. A note on modular spaces, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys., Volume 9 (1961), pp. 157-162

Cité par Sources :