Skip to main content
Have a personal or library account? Click to login
Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations Cover

Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations

Open Access
|Dec 2014

References

  1. [1] M. Aamri and D. El Moutawakil, Common fixed points under contractive con- ditions in symmetric spaces, Appl. Math. E-notes, 3, (2003), 156-162
  2. [2] M. Abbas and D. Dorić, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat, 24, (2010), 1-10
  3. [3] Ya. L. Alber and S. Guerre-Delabriere, Advances Appl., 98, 1997
  4. [4] A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type, J. Math. Anal. Appl., 322, (2006), 796-802
  5. [5] I. D. Arandjelović and D. Kečkić, Symmetric spaces approach to some fixed point results, Nonlinear Anal., 75, (2012), 5157-5168
  6. [6] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3, (1922), 133-181
  7. [7] R. Bellman and E. S. Lee, Functional equations in dynamic programming, Aequa- tiones Math., 17, (1978), 1-18
  8. [8] R. Bellman and B.S. Lee, Functional equations arising in dynamic programming, Aequationes Math., 17, (1978), 1-18
  9. [9] T. C. Bhakta and S. Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl., 98, (1984), 348-362
  10. [10] D. W. Boyd and R. S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20, (1969), 458-464
  11. [11] S. H. Cho, G. Y. Lee, and J. S. Bae, On coincidence and fixed-point theorems in symmetric spaces, Fixed Point Theory Appl., (2008), Article ID 562130
  12. [12] B. S. Choudhury, A common unique fixed point result in metric spaces involving generalized altering distances, Math. Comm., 10, (2005), 105-110
  13. [13] D. Doric, Common fixed point for generalized (Ψ;ϕ)-weak contractions, Appl. Math. Letter, 22, (2009), 1896-1900
  14. [14] P. N. Dutta and B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., (2008), Article ID 406368
  15. [15] F. Galvin and S. D. Shore, Completeness in semi-metric spaces, Pacific. J. Math., 113, (1984), 67-75
  16. [16] T. L. Hicks and B. E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal., 36, (1999), 331-344
  17. [17] M. Imdad and J. Ali, Common fixed point theorems in symmetric spaces employing a new implicit function and common property (E.A), Bull. Belg. Math. Soc. Simon Stevin, 16, (2009), 421-433
  18. [18] M. Imdad, J. Ali, and M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons Fractals, 42, (2009), 3121-3129
  19. [19] M. Imdad and A. H. Soliman, Some common fixed point theorems for a pair of tangential mappings in symmetric spaces, Appl. Math. Lett., 23, (2010), 351-355
  20. [20] M. Imdad, B. D. Pant, and S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST ) property and applications, J. Nonlinear Anal. Optim., 3, (2012), 225-237
  21. [21] M. Imdad and S. Chauhan, Employing common limit range property to prove unified metrical common fixed point theorems, Intern. J. Analysis, (2013), Article ID 763261
  22. [22] M. Imdad, S. Chauhan, and Z. Kadelburg, Fixed point theorems for mappings with common limit range property satisfying generalized ( ; ')-weak contractive con- ditions, Math. Sciences, 7, (2013), doi:10.1186/2251-7456-7-16
  23. [23] M. Imdad, S. Chauhan, Z. Kadelburg, and C. Vetro, Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application of functional equations in dynamic programming, Appl. Math. Comput., 227, (2014), 469-479
  24. [24] J. Jachymski, J. Matkowski, and T. Swiatkowski, Nonlinear contractions on semimetric spaces, J. Appl. Anal., 1, (1995), 125-134
  25. [25] M. Jovanović, Z. Kadelburg, and S. Radenović, Common fixed point re- sults in metric-type spaces, Fixed Point Theory Appl., (2010), Article ID 978121, doi:10.1155/2010/978121
  26. [26] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math.Math. Sci., 9, (1986), 771-779
  27. [27] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29, (1998), 227-238
  28. [28] Z. Kadelburg, S. Radenović, and N. Shahzad, A note on various classes of compatible-type pairs of mappings and common fixed point theorems, Abstract Appl.Anal., (2013), Article ID 697151
  29. [29] R. Kannan, Some results of fixed points, Bull. Calcutta Math. Soc., 60, (1968), 405-408
  30. [30] E. Karapιnar, D. K. Patel, M. Imdad, and D. Gopal, Some nonunique common fixed point theorems in symmetric spaces through CLRST property, Internat. J.Math. Math. Sci., (2013), Article ID 753965
  31. [31] M. S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30, (1984), 1-9
  32. [32] Y. Liu, J. Wu, and Z. Li, Common fixed points of single-valued and multivalued maps, Internat. J. Math. Math. Sci., 19, (2005), 3045-3055
  33. [33] Z. Liu and J.S. Ume, On properties of solutions for a class of functional equations arising in dynamic programming, J. Optim. Theory Appl., 117, (2003), 533
  34. [34] Z. Liu, L. Wong, H. Kug Kim, and S. M. Kang, Common fixed point theorems for contactive mappings and their applications in dynamic programming, Bull. Korean Math. Soc., 45, (2008), 573-585
  35. [35] D. Miheţ, A note on a paper of T. L. Hicks and B. E. Rhoades: Fixed point theory in symmetric spaces with applications to probabilistic spaces, [Nonlinear Anal. Ser. A: Theory Methods Appl., 36(3), 1999, 331-344], Nonlinear Anal., 65, (2006), 1411-1413
  36. [36] H. K. Nashine, New fixed point theorems for mappings satisfying generalized weakly contractive condition with weaker control functions, Ann. Polonici Math., 104, (2012), 109-119
  37. [37] R. P. Pant, Noncompatible mappings and common fixed points, Soochow J. Math., 26, (2000), 29-35
  38. [38] H. K. Pathak, Y. J. Cho, S. M. Kang, and B. S. Lee, Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming, Le Mate., 50, (1995), 15-33
  39. [39] H. K. Pathak and Deepmala, Some existing theorems for solvability of certain functional equations arising in dynamic programming, Bull. Cal. Math. Soc., 104, (2012), 237-244
  40. [40] H. K. Pathak and B. Fisher, Common fixed point theorems with applications in dynamic programming, Glasnik Mate., 31, (1996), 321-328
  41. [41] H. K. Pathak and R. Tiwari, Common fixed points for weakly compatible map- pings and applications in dynamic programming, Italian J. Pure Appl. Math., 30, (2013), 253-268
  42. [42] O. Popescu, Fixed point for (Ψ;ϕ)-weak contractions, Appl. Math. Lett., 24, (2011), 1-4
  43. [43] S. Radenović and Z. Kadelburg, Quasi-contractions on symmetric and cone sym- metric spaces, Banach J. Math. Anal., 5, (2011), 38-50
  44. [44] A. Razani and M. Yazdi, Two common fixed point theorems for compatible map- pings, Internat. J. Nonlinear Anal. Appl., 2, (2011), 7-18
  45. [45] S. Reich, Some fixed point problems, Atti. Accad. Naz. Lincei, 57, (1974), 194-198
  46. [46] S. Reich, Kannan's fixed point theorem, Boll. Un. Mat. Ital., 4, (1971), 1-11
  47. [47] B. E. Rhoades, A comparision of various definitions of contractive mappings, Rra.Ame. Math. Soc., 226, (1977), 257-290
  48. [48] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47, (2001), 2683-2693
  49. [49] S. Sessa, On a weak commutativity condition of mappings in fixed point considera- tions, Publ. Inst. Math. (Beograd)(N.S.), 32, (1982), 149-153
  50. [50] W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., (2011), Article ID 637958
  51. [51] C. Vetro, S. Chauhan, E. Karapιnar, and W. Shatanawi, Fixed points of weakly compatible mappings satisfying generalized φ-weak contractions, Bull.Malaysian Math. Sci. Soc., (2013), in press
  52. [52] Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contractions, Appl. Math. Lett., 22, (2009), 75-78
  53. [53] J. Zhu, Y. J. Cho, and S. M. Kang, Equivalent contractive conditions in sym- metric spaces, Comput. Math. Appl., 50, (2005), 1621-1628
  54. [54] W. A. Wilson, On semi-metric spaces, Amer. J. Math., 53, (1931), 361-373
DOI: https://doi.org/10.2478/awutm-2014-0007 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 95 - 120
Submitted on: Jan 24, 2014
Accepted on: Apr 24, 2014
Published on: Dec 11, 2014
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2014 Hemant Kumar Nashine, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.