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AN EXTENDED COUPLED COINCIDENCE POINT THEOREM AND RELATED RESULTS

Yıl 2016, Cilt: 34 Sayı: 4, 517 - 525, 01.12.2016

Öz

In this paper, we give an extended coupled coincidence point theorem for a mixed g-monotone mapping F:X→X satisfying a weaker contractive condition. As a result of this theorem, we introduce an extended coupled fixed point theorem. We also explain that there exist a relationship between Theorem 2.1 which is our main theorem and Theorem 1.3 introduced by Choudhury et. al. [ Choudhury, BS, Kundu, A: Appl. Math. Lett. 25,6-10(2012) ].

Kaynakça

  • [1] Freiwald R. C., “An introduction to set theory and topology”, Washington University in St. Louis. 2014. 449 pages.
  • [2] Ran ACM, Reurings MCB “A fixed point theorem in partially ordered sets and some applications to matrix equations”, Proc. Am.Math. Soc. 132, 1435-1443, 2004.
  • [3] Nieto JJ, Rodríguez-López R “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order 22, 223-239, 2005.
  • [4] Ćirić Lj Cakić, N Rajović, Ume J.S. ”Monotone generalized nonlinear contractions in partially ordered metric spaces”, Fixed Point Theory Appl, Article ID 131294, 2008.
  • [5] Choudhury B.S, Kundu A. “(ψ,α,β)-weak contractions in partially ordered metric spaces”, Appl Math Lett, 25, 6—10, 2012.
  • [6] Harjani J., Sadarangani K. “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations”, Nonlinear Anal. 72(2010), 1188-1197, 2010.
  • [7] Harandi A.A., Emami H. “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations”, Nonlinear Anal. 72(2010), 2238-2242, 2010.
  • [8] Bhaskar T.G., Lakshmikantham V. “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Anal. 65(2006), 1379-1393, 2006.
  • [9] Lakshmikantham V., Ćirić Lj Cakić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Anal. 70(2009), 4341—4349, 2009.
  • [10] Luong N.V., Thuan N.X., “Coupled fixed points in partially ordered metric spaces and application”, Nonlinear Anal. 74(2011), 983—992, 2011.
  • [11] Berinde, V., “Coupled fixed point theorems for ϕ-contractive mixed monotone mappings in partially ordered metric spaces”, Nonlinear Analysis 75 (2012) 3218—3228, 2012.
  • [12] Cho YJ., Rhoades B.E., Saadati R., Samet B., Shantawi W., “Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type”, Fixed Point Theory Appl, 8 (2012), 2012.
  • [13] Cho, Y.J., He G., Huang N.J., “The existence results of coupled quasi-solutions for a class of operator equations”, Bull.Korean Math. Soc. 47, 455-465, 2010.
  • [14] Abbas, M, Sintunavarat, W, Kumam, P: Coupled fixed point in partially ordered G-metric spaces. Fixed Point Theory Appl. 2012, 31 (2012).
Yıl 2016, Cilt: 34 Sayı: 4, 517 - 525, 01.12.2016

Öz

Kaynakça

  • [1] Freiwald R. C., “An introduction to set theory and topology”, Washington University in St. Louis. 2014. 449 pages.
  • [2] Ran ACM, Reurings MCB “A fixed point theorem in partially ordered sets and some applications to matrix equations”, Proc. Am.Math. Soc. 132, 1435-1443, 2004.
  • [3] Nieto JJ, Rodríguez-López R “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order 22, 223-239, 2005.
  • [4] Ćirić Lj Cakić, N Rajović, Ume J.S. ”Monotone generalized nonlinear contractions in partially ordered metric spaces”, Fixed Point Theory Appl, Article ID 131294, 2008.
  • [5] Choudhury B.S, Kundu A. “(ψ,α,β)-weak contractions in partially ordered metric spaces”, Appl Math Lett, 25, 6—10, 2012.
  • [6] Harjani J., Sadarangani K. “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations”, Nonlinear Anal. 72(2010), 1188-1197, 2010.
  • [7] Harandi A.A., Emami H. “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations”, Nonlinear Anal. 72(2010), 2238-2242, 2010.
  • [8] Bhaskar T.G., Lakshmikantham V. “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Anal. 65(2006), 1379-1393, 2006.
  • [9] Lakshmikantham V., Ćirić Lj Cakić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Anal. 70(2009), 4341—4349, 2009.
  • [10] Luong N.V., Thuan N.X., “Coupled fixed points in partially ordered metric spaces and application”, Nonlinear Anal. 74(2011), 983—992, 2011.
  • [11] Berinde, V., “Coupled fixed point theorems for ϕ-contractive mixed monotone mappings in partially ordered metric spaces”, Nonlinear Analysis 75 (2012) 3218—3228, 2012.
  • [12] Cho YJ., Rhoades B.E., Saadati R., Samet B., Shantawi W., “Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type”, Fixed Point Theory Appl, 8 (2012), 2012.
  • [13] Cho, Y.J., He G., Huang N.J., “The existence results of coupled quasi-solutions for a class of operator equations”, Bull.Korean Math. Soc. 47, 455-465, 2010.
  • [14] Abbas, M, Sintunavarat, W, Kumam, P: Coupled fixed point in partially ordered G-metric spaces. Fixed Point Theory Appl. 2012, 31 (2012).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Research Articles
Yazarlar

Mehmet Kır Bu kişi benim

Hukmi Kızıltunç Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Gönderilme Tarihi 8 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 34 Sayı: 4

Kaynak Göster

Vancouver Kır M, Kızıltunç H. AN EXTENDED COUPLED COINCIDENCE POINT THEOREM AND RELATED RESULTS. SIGMA. 2016;34(4):517-25.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/