Some approximate fixed point theorems without continuity of the operator using auxiliary functions
Sumit Chandok; Arslan Hojjat Ansari; Tulsi Dass Narang
Mathematica Bohemica (2019)
- Volume: 144, Issue: 3, page 251-271
- ISSN: 0862-7959
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topChandok, Sumit, Ansari, Arslan Hojjat, and Narang, Tulsi Dass. "Some approximate fixed point theorems without continuity of the operator using auxiliary functions." Mathematica Bohemica 144.3 (2019): 251-271. <http://eudml.org/doc/294623>.
@article{Chandok2019,
abstract = {We introduce partial generalized convex contractions of order $4$ and rank $4$ using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in $\alpha $-complete metric spaces and $\mu $-complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained. Some examples are also provided to illustrate the main results and to show the usability of the given hypotheses.},
author = {Chandok, Sumit, Ansari, Arslan Hojjat, Narang, Tulsi Dass},
journal = {Mathematica Bohemica},
keywords = {$\varepsilon $-fixed point; $\alpha $-admissible mapping; partial generalized convex contraction of order $4$ and rank $4$; $\alpha $-complete metric space},
language = {eng},
number = {3},
pages = {251-271},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some approximate fixed point theorems without continuity of the operator using auxiliary functions},
url = {http://eudml.org/doc/294623},
volume = {144},
year = {2019},
}
TY - JOUR
AU - Chandok, Sumit
AU - Ansari, Arslan Hojjat
AU - Narang, Tulsi Dass
TI - Some approximate fixed point theorems without continuity of the operator using auxiliary functions
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 3
SP - 251
EP - 271
AB - We introduce partial generalized convex contractions of order $4$ and rank $4$ using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in $\alpha $-complete metric spaces and $\mu $-complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained. Some examples are also provided to illustrate the main results and to show the usability of the given hypotheses.
LA - eng
KW - $\varepsilon $-fixed point; $\alpha $-admissible mapping; partial generalized convex contraction of order $4$ and rank $4$; $\alpha $-complete metric space
UR - http://eudml.org/doc/294623
ER -
References
top- Ansari, A. H., Shukla, S., Some fixed point theorems for ordered --contraction and subcontraction in 0--orbitally complete partial metric spaces, J. Adv. Math. Stud. 9 (2016), 37-53. (2016) Zbl1353.54030MR3495331
- Berinde, M., Approximate fixed point theorems, Stud. Univ. Babeş-Bolyai, Math. 51 (2006), 11-25. (2006) Zbl1164.54028MR2246435
- Browder, F. E., Petryshyn, W. V., 10.1090/S0002-9904-1966-11544-6, Bull. Am. Math. Soc. 72 (1966), 571-575. (1966) Zbl0138.08202MR0190745DOI10.1090/S0002-9904-1966-11544-6
- Chandok, S., Ansari, A. H., 10.23952/cot.2017.27, Comm. Opt. Theory 2017 (2017), Article ID 27, 12 pages. (2017) DOI10.23952/cot.2017.27
- Dey, D., Laha, A. K., Saha, M., 10.1155/2013/962058, J. Math. 2013 (2013), Article No. 962058, 4 pages. (2013) Zbl1268.54022MR3100732DOI10.1155/2013/962058
- Dey, D., Saha, M., Approximate fixed point of Reich operator, Acta Math. Univ. Comen., New Ser. 82 (2013), 119-123. (2013) Zbl1324.54067MR3028154
- Hussain, N., Kutbi, M. A., Salimi, P., 10.1155/2014/280817, Abstr. Appl. Anal. 2014 (2014), Article ID 280817, 11 pages. (2014) MR3166589DOI10.1155/2014/280817
- Istrăţescu, V. I., 10.1007/BF01761490, Ann. Mat. Pura Appl., IV. Ser. 130 (1982), 89-104. (1982) Zbl0477.54033MR0663966DOI10.1007/BF01761490
- Jaradat, M. M. M., Mustafa, Z., Ansari, A. H., Chandok, S., Dolićanin, Ć., 10.22436/jnsa.010.04.32, J. Nonlinear Sci. Appl. 10 (2017), 1695-1708. (2017) MR3639736DOI10.22436/jnsa.010.04.32
- Kohlenbach, U., Leuştean, L., 10.1016/j.na.2005.12.020, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66 (2007), 806-818. (2007) Zbl1118.47047MR2288433DOI10.1016/j.na.2005.12.020
- Latif, A., Sintunavarat, W., Ninsri, A., 10.11650/tjm.19.2015.4746, Taiwanese J. Math. 19 (2015), 315-333. (2015) Zbl1357.54034MR3313418DOI10.11650/tjm.19.2015.4746
- Miandaragh, M. A., Postolache, M., Rezapour, S., 10.1186/1687-1812-2013-255, Fixed Point Theory Appl. 2013 (2013), Article No. 255, 8 pages. (2013) Zbl1321.54089MR3213091DOI10.1186/1687-1812-2013-255
- Reich, S., 10.1016/0022-247X(78)90222-6, J. Math. Anal. Appl. 62 (1978), 104-113. (1978) Zbl0375.47031MR0514991DOI10.1016/0022-247X(78)90222-6
- Samet, B., Vetro, C., Vetro, P., 10.1016/j.na.2011.10.014, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75 (2012), 2154-2165. (2012) Zbl1242.54027MR2870907DOI10.1016/j.na.2011.10.014
- Tijs, S., Torre, A., Brânzei, R., Approximate fixed point theorems, Libertas Math. 23 (2003), 35-39 9999MR99999 2002283 . (2003) Zbl1056.47046MR2002283
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