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Coupled fixed point theorems under new coupled implicit relation in Hilbert spaces

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Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.
Wydawca
Rocznik
Strony
81--89
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
  • Mathematics Education, Kyungnam University, Changwon, Gyeongnam, 51767, Republic of Korea
Bibliografia
  • [1] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), 623–632.
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  • [3] H. Afshari, S. Kalantari, and E. Karapınar, Solution of fractional differential equations via coupled fixed point, Electron. J. Differ. Equ. 2015 (2015), 286.
  • [4] I. M. Erhan, E. Karapınar, A.-F. Roldán-López-de-Hierro, and N. Shahzad, Remarks on ‘Coupled coincidence point results for a generalized compatible pair with applications’, Fixed Point Theory Appl. 2014 (2014), 207, DOI: https://doi.org/10.1186/1687-1812-2014-207.
  • [5] S. Gülyaz and E. Karapınar, Coupled fixed point result in partially ordered partial metric spaces through implicit function, Hacet. J. Math. Stat. 42 (2013), no. 4, 347–357.
  • [6] B. Samet, E. Karapınar, H. Aydi, and V. C. Rajić, Discussion on some coupled fixed point theorems, Fixed Point Theory Appl. 2013 (2013), 50, DOI: https://doi.org/10.1186/1687-1812-2013-50.
  • [7] S. Gülyaz, E. Karapınar, and I. S. Yüce, A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation, Fixed Point Theory Appl. 2013 (2013), 38, DOI: https://doi.org/10.1186/1687-1812-2013-38.
  • [8] I. Beg and A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal. 71 (2009), no. 9, 3699–3704.
  • [9] I. Beg and A. R. Butt, Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces, Carpathian J. Math. 25 (2009), no. 1, 1–12.
  • [10] M. Nazam and Ö. Acar, Fixed points of (α ψ, )-contractions in Hausdorff partial metric spaces, Math. Methods Appl. Sci. 42 (2019), no. 16, 5159–5173, DOI: https://doi.org/10.1002/mma.5251.
  • [11] Ö. Acar, Generalization of (α F− d )-contraction on quasi-metric space, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 68 (2019), no. 1, 35–42, DOI: https://doi.org/10.31801/cfsuasmas.443587.
  • [12] A. S. Babu, T. Došenović, Md. M. Ali, S. Radenović, and K. P. R. Rao, Some Preśić type results in b-dislocated metric spaces, Constr. Math. Anal. 2 (2019), no. 1, 40–48, DOI: https://doi.org/10.33205/cma.499171.
  • [13] C. Vetro, A fixed-point problem with mixed-type contractive condition, Constr. Math. Anal. 3 (2020), no. 1, 45–52, DOI: https://doi.org/10.33205/cma.684638.
  • [14] L. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273.
  • [15] Lj. B. Ćirić, Generalized contractions and fixed point theorems, Publ. Inst. Math. (Beograd) (N.S.) 12 (1971), no. 26, 19–26.
  • [16] F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl. 20 (1967), 197–228.
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  • [23] M. Pitchaimani and D. R. Kumar, On construction of fixed point theory under implicit relation in Hilbert spaces, Nonlinear Func. Anal. Appl. 21 (2016), no. 3, 513–522.
  • [24] S. Chandok, E. Karapınar, and M. S. Khan, Existence and uniqueness of common coupled fixed point results via auxiliary functions, spaces, Bull. Iranian Math. Soc. 40 (2014), no. 1, 199–215.
  • [25] H. H. Alsulami, E. Karapınar, M. A. Kutbi, and A.-F. Roldán-López-de-Hierro, An illusion: “A Suzuki type coupled fixed point theorem”, Abstr. Appl. Anal. 2014 (2014), 235731, DOI: https://doi.org/10.1155/2014/235731.
  • [26] M. Pitchaimani and D. R. Kumar, Some common fixed point theorems using implicit relation in 2-Banach spaces, Surv. Math. Appl. 10 (2015), 159–168.
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Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
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Bibliografia
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