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Fs−contractive mappings in controlled metric type spaces

Year 2021, Volume: 4 Issue: 3, 149 - 158, 30.09.2021
https://doi.org/10.53006/rna.928319

Abstract

We investigate in this manuscript, we study a new type of mappings so called F_s −contractive, in addition
to we establish some fixed point results related to F_s −contractive type mappings in controlled type metric
spaces. Also, examples are provided to illustrate our results.

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Project Number

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Thanks

It is my pleasure to publish your journal

References

  • [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund Math. 3, 133-181 (1922).
  • [2] J. Jachymski, I. Jówik, On Kirk's asymptotic contractions. J Math Anal Appl. 300, 147-159 (2004). doi:10.1016/j. jmaa.2004.06.037.
  • [3] T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Non-linear Anal. 64, 971-978 (2006).
  • [4] N. Mlaiki, H. Aydi, N. Souayah and T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6, 194, 2018.
  • [5] A. Meir, E. Keeler, A theorem on contraction mappings. J Math Anal Appl. 28, 326-329 (1969). doi:10.1016/0022-247X (69)90031-6.
  • [6] T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces. Math Comput Mod- elling. 54, 2923-2927 (2011). doi:10.1016/j.mcm.2011.07.013.
  • [7] Choudhury, Binayak, S, Konar, P, Rhoades, BE, Metiya, N: Fixed point theorems for generalized weakly contractive mappings. Nonlinear Anal. 74, 2116-2126 (2011). doi:10.1016/j.na.2010.11.017.
  • [8] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, 94 (2012) https://doi.org/10.1186/1687-1812-2012-94.
  • [9] A. Lukács, S. Kajántó, Fixed point theorems for various types of F-contractions in complete b-metric spaces. Fixed Point Theory 19(1), 321-334 (2018). https://doi.org/10.24193/fpt-ro.2018.1.25. [10] S. Cobzas, Fixed points and completeness in metric and in generalized metric spaces (2016). arXiv:1508.05173v4 [math.FA] [11] T.K. Hu, On a fixed-point theorem for metric spaces. Am. Math. Mon. 74, 436-437 (1967).
  • [12] H. Garai, T. Senapati, L.K. Dey, A study on Kannan type contractive mappings (2017). arXiv:1707.06383v1 [math.FA].
  • [13] F.E. Browder, W.V. Petryshyn, The solution by iteration of non-linear functional equations in Banach spaces. Bull. Am. Math. Soc. 72, 571-575 (1966).
  • [14] J.B. Baillon, R.E. Bruck, S. Reich, On the asymptotic behaviour of non-expansive mappings and semi-groups in Banach spaces. Houst. J. Math. 4, 1-9 (1978).
  • [15] R.E. Bruck, S. Reich, Non-expansive projections and resolvents of accretive operators in Banach spaces. Houst. J. Math. 3, 459-470 (1977).
  • [16] J. Górnicki, Fixed point theorems for F-expanding mappings. Fixed Point Theory Appl. 2017, 9 (2017). https://doi.org/10.1186/s13663-017-0602-3.
  • [17] T. Abdeljawad, N. Mlaiki, H. Aydi, and N. Souayah, Double Controlled Metric Type Spaces and Some Fixed Point Results, Mathematics 2018, 6, 320; doi:10.3390/math6120320
  • [18] E. Karapinar, S. Czerwik, H. Aydi, (α,ψ)-Meir-Keeler contraction mappings in generalized b-metric spaces, Journal of Function spaces, Volume 2018 (2018), Article ID 3264620, 4 pages.
  • [19] H. Afshari, H. Aydi, E. Karapinar, On generalized α − ψ-Geraghty contractions on b-metric spaces, Georgian Math. J. 27 (2020), 9-21
  • [20] E. Karapinar, A. Petrusel, and G.Petrusel, On admissible hybrid Geraghty contractions, Carpathian J. Math. 36 (2020), No. 3, 433 - 442.
  • [21] H. Aydi, M. F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012 :88.
  • [22] H. Aydi, M.F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed Point Theory, 13 (2) (2012), 337-346.
  • [23] M.A. Alghamdi, S. Gulyaz-Ozyurt and E. Karapinar, A Note on Extended Z−Contraction, Mathematics, Volume 8 Issue 2 Article Number 195 (2020).
Year 2021, Volume: 4 Issue: 3, 149 - 158, 30.09.2021
https://doi.org/10.53006/rna.928319

Abstract

Project Number

none

References

  • [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund Math. 3, 133-181 (1922).
  • [2] J. Jachymski, I. Jówik, On Kirk's asymptotic contractions. J Math Anal Appl. 300, 147-159 (2004). doi:10.1016/j. jmaa.2004.06.037.
  • [3] T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Non-linear Anal. 64, 971-978 (2006).
  • [4] N. Mlaiki, H. Aydi, N. Souayah and T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6, 194, 2018.
  • [5] A. Meir, E. Keeler, A theorem on contraction mappings. J Math Anal Appl. 28, 326-329 (1969). doi:10.1016/0022-247X (69)90031-6.
  • [6] T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces. Math Comput Mod- elling. 54, 2923-2927 (2011). doi:10.1016/j.mcm.2011.07.013.
  • [7] Choudhury, Binayak, S, Konar, P, Rhoades, BE, Metiya, N: Fixed point theorems for generalized weakly contractive mappings. Nonlinear Anal. 74, 2116-2126 (2011). doi:10.1016/j.na.2010.11.017.
  • [8] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, 94 (2012) https://doi.org/10.1186/1687-1812-2012-94.
  • [9] A. Lukács, S. Kajántó, Fixed point theorems for various types of F-contractions in complete b-metric spaces. Fixed Point Theory 19(1), 321-334 (2018). https://doi.org/10.24193/fpt-ro.2018.1.25. [10] S. Cobzas, Fixed points and completeness in metric and in generalized metric spaces (2016). arXiv:1508.05173v4 [math.FA] [11] T.K. Hu, On a fixed-point theorem for metric spaces. Am. Math. Mon. 74, 436-437 (1967).
  • [12] H. Garai, T. Senapati, L.K. Dey, A study on Kannan type contractive mappings (2017). arXiv:1707.06383v1 [math.FA].
  • [13] F.E. Browder, W.V. Petryshyn, The solution by iteration of non-linear functional equations in Banach spaces. Bull. Am. Math. Soc. 72, 571-575 (1966).
  • [14] J.B. Baillon, R.E. Bruck, S. Reich, On the asymptotic behaviour of non-expansive mappings and semi-groups in Banach spaces. Houst. J. Math. 4, 1-9 (1978).
  • [15] R.E. Bruck, S. Reich, Non-expansive projections and resolvents of accretive operators in Banach spaces. Houst. J. Math. 3, 459-470 (1977).
  • [16] J. Górnicki, Fixed point theorems for F-expanding mappings. Fixed Point Theory Appl. 2017, 9 (2017). https://doi.org/10.1186/s13663-017-0602-3.
  • [17] T. Abdeljawad, N. Mlaiki, H. Aydi, and N. Souayah, Double Controlled Metric Type Spaces and Some Fixed Point Results, Mathematics 2018, 6, 320; doi:10.3390/math6120320
  • [18] E. Karapinar, S. Czerwik, H. Aydi, (α,ψ)-Meir-Keeler contraction mappings in generalized b-metric spaces, Journal of Function spaces, Volume 2018 (2018), Article ID 3264620, 4 pages.
  • [19] H. Afshari, H. Aydi, E. Karapinar, On generalized α − ψ-Geraghty contractions on b-metric spaces, Georgian Math. J. 27 (2020), 9-21
  • [20] E. Karapinar, A. Petrusel, and G.Petrusel, On admissible hybrid Geraghty contractions, Carpathian J. Math. 36 (2020), No. 3, 433 - 442.
  • [21] H. Aydi, M. F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012 :88.
  • [22] H. Aydi, M.F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed Point Theory, 13 (2) (2012), 337-346.
  • [23] M.A. Alghamdi, S. Gulyaz-Ozyurt and E. Karapinar, A Note on Extended Z−Contraction, Mathematics, Volume 8 Issue 2 Article Number 195 (2020).
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Muhib Abuloha This is me

Doaa Rizk 0000-0002-4547-3165

Kamaleldin Abodayeh

Aiman Mukheimer This is me

Nizar Souayah

Project Number none
Publication Date September 30, 2021
Published in Issue Year 2021 Volume: 4 Issue: 3

Cite

APA Abuloha, M., Rizk, D., Abodayeh, K., Mukheimer, A., et al. (2021). Fs−contractive mappings in controlled metric type spaces. Results in Nonlinear Analysis, 4(3), 149-158. https://doi.org/10.53006/rna.928319
AMA Abuloha M, Rizk D, Abodayeh K, Mukheimer A, Souayah N. Fs−contractive mappings in controlled metric type spaces. RNA. September 2021;4(3):149-158. doi:10.53006/rna.928319
Chicago Abuloha, Muhib, Doaa Rizk, Kamaleldin Abodayeh, Aiman Mukheimer, and Nizar Souayah. “Fs−contractive Mappings in Controlled Metric Type Spaces”. Results in Nonlinear Analysis 4, no. 3 (September 2021): 149-58. https://doi.org/10.53006/rna.928319.
EndNote Abuloha M, Rizk D, Abodayeh K, Mukheimer A, Souayah N (September 1, 2021) Fs−contractive mappings in controlled metric type spaces. Results in Nonlinear Analysis 4 3 149–158.
IEEE M. Abuloha, D. Rizk, K. Abodayeh, A. Mukheimer, and N. Souayah, “Fs−contractive mappings in controlled metric type spaces”, RNA, vol. 4, no. 3, pp. 149–158, 2021, doi: 10.53006/rna.928319.
ISNAD Abuloha, Muhib et al. “Fs−contractive Mappings in Controlled Metric Type Spaces”. Results in Nonlinear Analysis 4/3 (September 2021), 149-158. https://doi.org/10.53006/rna.928319.
JAMA Abuloha M, Rizk D, Abodayeh K, Mukheimer A, Souayah N. Fs−contractive mappings in controlled metric type spaces. RNA. 2021;4:149–158.
MLA Abuloha, Muhib et al. “Fs−contractive Mappings in Controlled Metric Type Spaces”. Results in Nonlinear Analysis, vol. 4, no. 3, 2021, pp. 149-58, doi:10.53006/rna.928319.
Vancouver Abuloha M, Rizk D, Abodayeh K, Mukheimer A, Souayah N. Fs−contractive mappings in controlled metric type spaces. RNA. 2021;4(3):149-58.