456
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Coupled coincidence point results for probabilistic φ-contractions

, & | (Reviewing Editor)
Article: 1204069 | Received 18 Feb 2016, Accepted 29 May 2016, Published online: 14 Jul 2016

References

  • Bhaskar, T. G., & Lakshmikantham, V. (2006). Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Analysis, 65, 1379–1393.
  • Choudhury, B. S., & Das, K. P. (2009). A coincidence point result in Menger spaces using a control function. Chaos, Solitons and Fractals, 42, 3058–3063.
  • Choudhury, B. S., & Das, P. (2014). Coupled coincidence point results for compatible mappings in partially ordered probabilistic metric spaces. Asian-European Journal of Mathematics, 7, 1450009.
  • Choudhury, B. S., & Kundu, A. (2010). A coupled coincidence point result in partially ordered metric spaces for compatible mappings. Nonlinear Analysis, 73, 2524–2531.
  • Chang, S. S., Cho, Y. J., & Kang, S. M. (1994). Probablistic metric spaces and nonlinear operator theory. Chengdu, China: Sichuan University Press.
  • \’{C}iri\’{c}, L. (2010). Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces. Nonlinear Analysis, 72, 2009–2018.
  • \’{C}iri\’{c}, L., Agarwal, R. P., & Samet, B. (2011). Mixed monotone generalized contractions in partially ordered probabilistic metric spaces. Fixed Point Theory and Applications, 2011, 56.
  • Doric, D. (2013). Nonlinear coupled coincidence and coupled fixed point theorems for not necessary commutative contractive mappings in partially ordered probabilistic metric spaces. Applied Mathematics and Computation, 219, 5926–5935.
  • Fang, J. X. (2009). Common fixed point theorems of compatible and weak compatible maps in Menger spaces. Nonlinear Analysis, 71, 1833–1843.
  • Fang, J. X. (2015). On φ- contractions in probabilistic and fuzzy metric spaces. Fuzzy Sets and Systems, 267, 86–99. doi:10.1016/j.fss.2014.06.013
  • Guo, D., & Lakshmikantham, V. (1987). Coupled fixed points of nonlinear operators with applications. Nonlinear Analysis, 11, 623–632.
  • Had\u{z}i\’{c}, O., & Pap, E. (2001). Fixed point theory in probabilistic metric spaces. Dordrecht: Kluwer Academic Publishers.
  • Hu, X. Q., & Ma, X. Y. (2011). Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces. Nonlinear Analysis, 74, 6451–6458.
  • Jachymski, J. (2010). On probabilistic φ- contractions on Menger spaces. Nonlinear Analysis, 73, 1131–1137.
  • Lakshmikantham, V., & \’{C}iri\’{c}, L. (2009). Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Analysis, 70, 4341–4349.
  • Luong, N. V., & Thuan, N. X. (2011). Coupled fixed points in partially ordered metric spaces and application. Nonlinear Analysis, 74, 983–992.
  • Mursaleem, M., Mohiuddine, S. A., & Agarwal, R. P. (2012). Coupled fixed point theorems for φ contractive type mappings in partially ordered metric spaces. Fixed Point Theory and Applications, 2012, 228.
  • Mohiuddine, S. A., & Alotaibi, A. (2012). On coupled fixed point theorems for nonlinear contractions in partially ordered φ- metric spaces. Abstract and Applied Analysis, 2012, 15. Art. ID 897198
  • O’Regan, D., & Saadati, R. (2008). Nonlinear contraction theorems in probabilistic spaces. Applied Mathematics and Computation, 195, 86–93.
  • Samet, B. (2010). Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces. Nonlinear Analysis, 72, 4508–4517.
  • Schweizer, B., & Sklar, A. (1983). Probabilistic metric spaces. North-Holland: Elsevier.
  • Sehgal, V. M., & Bharucha-Reid, A. T. (1972). Fixed point of contraction mappings on PM space. Theory of Computing Systems, 6, 97–100.
  • Xiao, J. Z., Zhu, X. H., & Cao, Y. F. (2011). Common coupled fixed point results for probabilistic φ-contractions in Menger spaces. Nonlinear Analysis, 74, 4589–4600.