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Title: Hardy-Rogers-type fixed point theorems for $\alpha $-$GF$-contractions (English)
Author: Arshad, Muhammad
Author: Ameer, Eskandar
Author: Hussain, Aftab
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 51
Issue: 3
Year: 2015
Pages: 129-141
Summary lang: English
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Category: math
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Summary: The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for $\alpha $-$\eta $-$GF$-contraction in a complete metric space. We extend the concept of $F$-contraction into an $\alpha $-$\eta $-$GF$-contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results. (English)
Keyword: metric space
Keyword: fixed point
Keyword: $F$-contraction
Keyword: $\alpha $-$\eta $-$GF$-contraction of Hardy-Rogers-type
MSC: 46S40
MSC: 47H10
MSC: 54H25
idZBL: Zbl 06487025
idMR: MR3397266
DOI: 10.5817/AM2015-3-129
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Date available: 2015-09-09T09:42:30Z
Last updated: 2016-04-02
Stable URL: http://hdl.handle.net/10338.dmlcz/144423
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Reference: [1] Abdeljawad, T.: Meir-Keeler $\alpha $-contractive fixed and common fixed point theorems.Fixed Point Theory Appl. (2013). DOI: http://dx.doi.org/10.1186/1687-1812-2013-19 Zbl 1295.54038, MR 3022841, 10.1186/1687-1812-2013-19
Reference: [2] Arshad, M., Fahimuddin, , Shoaib, A., Hussain, A.: Fixed point results for $\alpha $-$\psi $-locally graphic contraction in dislocated quasi metric spaces.Mathematical Sciences (2014), 7 pp. DOI: http://dx.doi.org/10.1007/s40096-014-0132 10.1007/s40096-014-0132
Reference: [3] Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux equations itegrales.Fund. Math. 3 (1922), 133–181.
Reference: [4] Ćirić, L.B.: A generalization of Banach’s contraction principle.Proc. Amer. Math. Soc. 45 (1974), 267–273. Zbl 0291.54056, MR 0356011, 10.2307/2040075
Reference: [5] Cosentino, M., Vetro, P.: Fixed point results for $F$-contractive mappings of Hardy-Rogers-type.Filomat 28 (4) (2014), 715–722. DOI: http://dx.doi.org/10.2298/FIL 1404715C MR 3360064, 10.2298/FIL1404715C
Reference: [6] Edelstein, M.: On fixed and periodic points under contractive mappings.J. Lond. Math. Soc. 37 (1962), 74–79. Zbl 0113.16503, MR 0133102, 10.1112/jlms/s1-37.1.74
Reference: [7] Fisher, B.: Set-valued mappings on metric spaces.Fund. Math. 112 (2) (1981), 141–145. Zbl 0479.54026, MR 0619490
Reference: [8] Geraghty, M.: On contractive mappings.Proc. Amer. Math. Soc. 40 (1973), 604–608. Zbl 0245.54027, MR 0334176, 10.1090/S0002-9939-1973-0334176-5
Reference: [9] Hussain, N., Al-Mezel, S., Salimi, P.: Fixed points for $\alpha $-$\psi $-graphic contractions with application to integral equations.Abstr. Appl. Anal. (2013), Article 575869. MR 3108673
Reference: [10] Hussain, N., Arshad, M., Shoaib, A., Fahimuddin, : Common fixed point results for $\alpha $-$\psi $-contractions on a metric space endowed with graph.J. Inequal. Appl. 136 (2014). Zbl 1310.54050, MR 3284402
Reference: [11] Hussain, N., Karapınar, E., Salimi, P., Akbar, F.: $\alpha $-admissible mappings and related fixed point theorems.J. Inequal. Appl. 114 (2013), 1–11. Zbl 1293.54023, MR 3047105
Reference: [12] Hussain, N., Karapınar, E., Salimi, P., Vetro, P.: Fixed point results for $G^{m}$-Meir-Keeler contractive and $G$-$(\alpha ,\psi )$-Meir-Keeler contractive mappings.Fixed Point Theory Appl. 34 (2013). Zbl 1293.54024
Reference: [13] Hussain, N., Kutbi, M.A., Salimi, P.: Fixed point theory in $\alpha $-complete metric spaces with applications.Abstr. Appl. Anal. (2014), 11pp., Article ID 280817. MR 3166589
Reference: [14] Hussain, N., Salimi, P.: Suzuki-Wardowski type fixed point theorems for $\alpha $-$GF$-contractions.Taiwanese J. Math. 18 (6) (2014), 1879–1895. DOI: http://dx.doi.org/10.11650/tjm.18.2014.4462 MR 3284036, 10.11650/tjm.18.2014.4462
Reference: [15] Hussain, N., Salimi, P., Latif, A.: Fixed point results for single and set-valued $\alpha $-$\eta $-$\psi $-contractive mappings.Fixed Point Theory Appl. 212 (2013). Zbl 1293.54025, MR 3103005
Reference: [16] Karapınar, E., Samet, B.: Generalized $(\alpha -\psi )$ contractive type mappings and related fixed point theorems with applications.Abstr. Appl. Anal. (2012), Article ID 793486. Zbl 1252.54037, MR 2965472
Reference: [17] Kutbi, M.A., Arshad, M., Hussain, A.: On modified $\alpha $-$\eta $-contractive mappings.Abstr. Appl. Anal. 2014 (2014), 7pp., Article ID 657858. MR 3246349
Reference: [18] Nadler, S.B.: Multivalued contraction mappings.Pacific J. Math. 30 (1969), 475–488. MR 0254828, 10.2140/pjm.1969.30.475
Reference: [19] Piri, H., Kumam, P.: Some fixed point theorems concerning $F$-contraction in complete metric spaces.Fixed Point Theory Appl. 210 (2014). MR 3357360
Reference: [20] Salimi, P., Latif, A., Hussain, N.: Modified $\alpha $-$\psi $-contractive mappings with applications.Fixed Point Theory Appl. 151 (2013). Zbl 1293.54036, MR 3074018
Reference: [21] Samet, B., Vetro, C., Vetro, P.: Fixed point theorems for $\alpha $-$\psi $-contractive type mappings.Nonlinear Anal. 75 (2012), 2154–2165. Zbl 1242.54027, MR 2870907, 10.1016/j.na.2011.10.014
Reference: [22] Secelean, N.A.: Iterated function systems consisting of $F$-contractions.Fixed Point Theory Appl. (2013), Article ID 277 (2013). DOI: http://dx.doi.org/10.1186/1687-1812-2013-277 MR 3213104, 10.1186/1687-1812-2013-277
Reference: [23] Sgroi, M., Vetro, C.: Multi-valued $F$-contractions and the solution of certain functional and integral equations.Filomat 27 (7) (2013), 1259–1268. MR 3243997, 10.2298/FIL1307259S
Reference: [24] Wardowski, D.: Fixed point theory of a new type of contractive mappings in complete metric spaces.Fixed Point Theory Appl. (2012), Article ID 94 (2012). MR 2949666
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