Tripled Fixed Point Results for T-Contractions on Abstract Metric Spaces

Article Sidebar

PDF
Cite as:
Hamidreza Rahimi, Calogero Vetro, Mujahid Abbas, Ghasem Soleimani Rad, Tripled Fixed Point Results for T-Contractions on Abstract Metric Spaces, Int. J. Anal. Appl., 6 (2) (2014), 132-138.

Main Article Content

Hamidreza Rahimi, Calogero Vetro, Mujahid Abbas, Ghasem Soleimani Rad

Abstract

In this paper we introduce the notion of T-contraction for tripled fixed points in abstract metric spaces and obtain some tripled fixed point theorems which extend and generalize well-known comparable results in the literature. To support our results, we present an example and an applications to integral equations.

Article Details

References

  1. M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008) 416-420.
  2. M. Abbas, B.E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (2009) 511-515.
  3. H. Aydi, M. Abbas, W. Sintunavarat, P. Kumam, Tripled fixed point of W-compatible mappings in abstract metric spaces, Fixed Point Theory Appl. 2012, 2012:134.
  4. H. Aydi, E. Karapinar, M. Postolache, Tripled coincidence point theorems for weak φ- contractions in partially ordered metric spaces, Fixed Point Theory Appl. (in press).
  5. S. Banach, Sur les op ´erations dans les ensembles abstraits et leur application aux ´equations int ´egrales, Fund. Math. J. 3 (1922) 133-181.
  6. A. Beiranvand, S. Moradi, M. Omid, H. Pazandeh, Two fixed point theorems for special mappings, arxiv:0903.1504v1 math FA. (2009).
  7. V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889-4897.
  8. T. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393.
  9. L.B. Ciri ´c, A generalization of Banach contraction principle, Proc. Amer. Math. Soc. 45 ´ (1974) 267-273.
  10. M. Filipovi ´c, L. Paunovi ´c, S. Radenovi ´c, M. Rajovi ´c, Remarks on “Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings”, Math. Comput. Modelling 54 (2011) 1467-1472.
  11. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
  12. L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1467-1475.
  13. G. Jungck, Commuting maps and fixed points, Amer. Math. Monthly 83 (1976) 261-263.
  14. V. Lakshmikanthama, L. Ciri ´c, Coupled fixed point theorems for nonlinear contractions in ´ partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341-4349.
  15. S. Moradi, Kannan fixed-point theorem on complete metric spaces and generalized metric spaces depended an another function, Int. J. Math. Anal. 5 (47) (2011) 2313-2320.
  16. J.R. Morales, E. Rojas, Cone metric spaces and fixed point theorems of T-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175-184.
  17. E.M. Mukhamadiev, V.J. Stetsenko, Fixed point principle in generalized metric space, Izvestija AN Tadzh. SSR, fiz.-mat.igeol.-chem.nauki. 10 (4) (1969) 8-19 (in Russian).
  18. A.I. Perov, The Cauchy problem for systems of ordinary differential equations, Approximate Methods of Solving Differential Equations, Kiev. Nauk. Dum. (1964) 115-134 (in Russian).
  19. H. Rahimi, B.E. Rhoades, S. Radenovi ´c, G. Soleimani Rad, Fixed and periodic point theorems for T-contractions on cone metric spaces, Filomat 27 (5) (2013) 881-888.
  20. H. Rahimi, G. Soleimani Rad, Fixed point theory in various spaces, Lambert Academic Publishing (LAP), Germany, 2013.
  21. H. Rahimi, G. Soleimani Rad, New fixed and periodic point results on cone metric spaces, Journal of Linear and Topological Algebra 1 (1) (2012) 33-40.
  22. S. Rezapour, R. Hamlbarani, Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008) 719-724.
  23. B.E. Rhoades, A comparison of various definition of contractive mappings, Trans. Amer. Math. Soc. 266 (1977) 257-290.
  24. F. Sabetghadam, H.P. Masiha, A.H. Sanatpour, Some coupled fixed point theorems in cone metric space, Fixed Point Theory Appl. 2009 (2009), Article ID 125426, 8 pages.
  25. B. Samet, C. Vetro, Coupled fixed point, f-invariant set and fixed point of N-order, Ann. Funct. Anal. 1 (2) (2010) 46-56.
  26. P.P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math. 48 (1997) 825- 859.