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$\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications

Yıl 2018, Cilt: 1 Sayı: 2, 212 - 219, 25.12.2018

Ekber Girgin Mahpeyker Öztürk

https://doi.org/10.33401/fujma.492561
Cited By: 1

Öz

In this article, we establish $\alpha_\kappa-$implicit contraction and provide some fixed point results in non-AMMS. Our results progress and generalize some famous consequences in a suitable resource. As an implementation, we study stability in the sense of Ulam-Hyers and a fixed point problem's well-posedness. In addition, some examples are given for new concepts. Also, an application to integral equations is discussed.

Anahtar Kelimeler

non-Archimedean modular metric space Implicit contraction Ulam-Hyers stability Well-posedness

Kaynakça

  • [1] V. V. Chistyakov, Modular metric spaces, I: Basic concepts, Nonlinear Anal., 72 (2010), 1-14.
  • [2] V. V. Chistyakov, Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15-30.
  • [3] C. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl. 2011(93) (2011) ,9 pages.
  • [4] M. Paknazar, M. A. Kutbi, M. Demma, P. Salimi, On non-Archimedean Modular metric space and some nonlinear contraction mappings, J. Nonlinear Sci. Appl., (2017), in press.
  • [5] V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacau, 7 (1997), 129-133.
  • [6] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for $\alpha-\psi-$contractive type mappings, Nonlinear Analysis, 75 (2012) (2012), 2154-2165.
  • [7] H. Aydi, $\alpha-$implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations, J. Nonlinear Convex Anal., 17(12) (2015), 2417-2433.
  • [8] A. Hussain, T. Kanwal, Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point, Transections of A. Razmadze Mathematical Enstitute, 172(3) (2018), 48-490.
  • [9] M. Abbas, A. Hussain, B. Popovic, S. Radenovic, Istratescu-Suzuki-Ciric type fixed point results in thee framework of G-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 6077-6095.
  • [10] N. Hussain, C. Vetro, F. Vetro, Fixed point results for $\alpha-$implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21(3) (2016), 362-378.
  • [11] V. Berinde, Approximating fixed points of implicit almost contractions, Hacet. J. Math. Stat., 41 (2012), 93-102.

Yıl 2018, Cilt: 1 Sayı: 2, 212 - 219, 25.12.2018

Ekber Girgin Mahpeyker Öztürk

https://doi.org/10.33401/fujma.492561
Cited By: 1

Öz

Kaynakça

  • [1] V. V. Chistyakov, Modular metric spaces, I: Basic concepts, Nonlinear Anal., 72 (2010), 1-14.
  • [2] V. V. Chistyakov, Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15-30.
  • [3] C. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl. 2011(93) (2011) ,9 pages.
  • [4] M. Paknazar, M. A. Kutbi, M. Demma, P. Salimi, On non-Archimedean Modular metric space and some nonlinear contraction mappings, J. Nonlinear Sci. Appl., (2017), in press.
  • [5] V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacau, 7 (1997), 129-133.
  • [6] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for $\alpha-\psi-$contractive type mappings, Nonlinear Analysis, 75 (2012) (2012), 2154-2165.
  • [7] H. Aydi, $\alpha-$implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations, J. Nonlinear Convex Anal., 17(12) (2015), 2417-2433.
  • [8] A. Hussain, T. Kanwal, Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point, Transections of A. Razmadze Mathematical Enstitute, 172(3) (2018), 48-490.
  • [9] M. Abbas, A. Hussain, B. Popovic, S. Radenovic, Istratescu-Suzuki-Ciric type fixed point results in thee framework of G-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 6077-6095.
  • [10] N. Hussain, C. Vetro, F. Vetro, Fixed point results for $\alpha-$implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21(3) (2016), 362-378.
  • [11] V. Berinde, Approximating fixed points of implicit almost contractions, Hacet. J. Math. Stat., 41 (2012), 93-102.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ekber Girgin 0000-0002-8913-5416

Mahpeyker Öztürk 0000-0003-2946-6114

Yayımlanma Tarihi 25 Aralık 2018
Gönderilme Tarihi 5 Aralık 2018
Kabul Tarihi 23 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Girgin, E., & Öztürk, M. (2018). $\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications. Fundamental Journal of Mathematics and Applications, 1(2), 212-219. https://doi.org/10.33401/fujma.492561
AMA Girgin E, Öztürk M. $\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications. FUJMA. Aralık 2018;1(2):212-219. doi:10.33401/fujma.492561
Chicago Girgin, Ekber, ve Mahpeyker Öztürk. “$\alpha_\kappa-$Implicit Contraction in Non-AMMS With Some Applications”. Fundamental Journal of Mathematics and Applications 1, sy. 2 (Aralık 2018): 212-19. https://doi.org/10.33401/fujma.492561.
EndNote Girgin E, Öztürk M (01 Aralık 2018) $\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications. Fundamental Journal of Mathematics and Applications 1 2 212–219.
IEEE E. Girgin ve M. Öztürk, “$\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications”, FUJMA, c. 1, sy. 2, ss. 212–219, 2018, doi: 10.33401/fujma.492561.
ISNAD Girgin, Ekber - Öztürk, Mahpeyker. “$\alpha_\kappa-$Implicit Contraction in Non-AMMS With Some Applications”. Fundamental Journal of Mathematics and Applications 1/2 (Aralık 2018), 212-219. https://doi.org/10.33401/fujma.492561.
JAMA Girgin E, Öztürk M. $\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications. FUJMA. 2018;1:212–219.
MLA Girgin, Ekber ve Mahpeyker Öztürk. “$\alpha_\kappa-$Implicit Contraction in Non-AMMS With Some Applications”. Fundamental Journal of Mathematics and Applications, c. 1, sy. 2, 2018, ss. 212-9, doi:10.33401/fujma.492561.
Vancouver Girgin E, Öztürk M. $\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications. FUJMA. 2018;1(2):212-9.

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