C-Class Functions on Shorter Proofs of Some Even-Tupled Coincidence Theorems in Ordered Metric Spaces

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Anupam Sharma

Abstract

The purpose of this paper is to prove some even tupled coincidence theorems for mappings with one variable in ordered complete metric spaces by using the concept of C-class functions. Our results generalize and improve several results in the literature.

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References

  1. Agarwal, R. P., El-Gebeily, M. A., ORegan, D: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87(1) (2008), 109-116.
  2. Altun, I. and Simsek, H: Some fixed point theorems on ordered metric spaces and application. Fixed Point Theory Appl. 2010 (2010), Article ID 621469.
  3. Ansari, A. H.: Note on (φ,ψ)-contractive type mappings and related fixed point. The 2nd Regional Conference on Mathematics And Applications, PNU, (2014) , 377-380.
  4. Berinde, V. and Borcut, M., Tripled fixed point theorems for contractive type mappings partially ordered metric spaces. Nonlinear Anal., 75 (15) (2011), 4889-4897.
  5. Bhaskar, T. G., Lakshmikantham, V.: Fixed points theorems in partially ordered metric spaces and applications. Nonlinear Anal. TMA 65 (2006), 1379-1393.
  6. Berzig, M. and Samet, B.: An extension of coupled fixed point's concept in higher dimension and applications. Comput. Math. Appl., 63 (2012), 1319-1334.
  7. Caballero, J., Harjani, J. and Sadarangani, K: Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations. Fixed Point Theory Appl. 2010 (2010), Article ID 916064.
  8. Choudhury, B. S., Metiya, N. and Kundu, A.: Coupled coincidence point theorems in ordered metric spaces. Ann. Univ. Ferrara 57 (2011), 1-16.
  9. Dalal, S., Khan, L. A., Masmali, I. and Radenovic, S.: Some remarks on multidimensional fixed point theorems in partially ordered metric spaces, J. Adv. Math. 7 (1) (2014), 1084-1094.
  10. Guo, D. J. and Lakshmikantham, V.: Coupled fixed points of nonlinear operators with applications. Nonlinear Anal. 11 (1987), no. 5, 623-632.
  11. Harandi, A. A. and Emami, H: A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. Nonlinear Anal. 72(5) (2010), 2238-2242.
  12. Harjani, J.and Sadarangani, K: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 71(7-8) (2009), 3403-3410.
  13. Harjani, J. and Sadarangani, K: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal. 72 (2010), 1188-1197.
  14. Imdad, M., Sharma, A. and Rao, K. P. R.: n-tupled coincidence and common fixed point results for weakly con- tractive mappings in complete metric spaces. Bull. Math. Anal. Appl., 5(4) (2013), 19-39.
  15. Imdad, M., Sharma, A. and Rao, K. P. R.: Generalized n-tupled fixed point theorems for nonlinear contraction mapping. Afrika Matematika, 26 (2015), 443455.
  16. Imdad, M., Soliman, A. H., Choudhury, B. S. and Das, P.: On n-tupled coincidence and common fixed points results in metric spaces. Jour. of Operators, 2013 (2013), Article ID 532867, 9 pages.
  17. Imdad, M., Alam, A. and Soliman, A. H.: Remarks on a recent general even-tupled coincidence theorem. J. Adv. Math. 9 (1) (2014), 1787-1805.
  18. Jachymski, J: Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Anal. 74(3) (2011), 768-774.
  19. Jleli, M., Raji ´ c, V. ´ C., Samet, B. and Vetro, C.: Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations. J. Fixed Point Theory Appl. 12 (2012), 175-192.
  20. Karapinar, E., Roldan, A., Martinez-Moreno, J. and Roldan, C.: Meir-Keeler type multidimensional fixed point theorems in partially ordered metric spaces, Abstract and Applied Analysis, 2013 (2013), Article ID 406026.
  21. Khan, M. S., Swaleh, M., Sessa, S.: Fixed point theorems by altering distance functions between the points. Bull. Aust. Math. Soc. 30 (1984), 1-9.
  22. Kutbi, M. A., Roldán, A., Sintunavarat, W., Moreno, J. M. and Roldán, C.: F-closed sets and coupled fixed point theorems without the mixed monotone property. Fixed point theory and applications, 2013 (2013), Article ID 330.
  23. Lakshmikantham, V. and ´ Ciri ´ c, Lj. B.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70 (2009), 4341-4349.
  24. Nashine, H. K. and Altun, I: A common fixed point theorem on ordered metric spaces. Bull. Iran. Math. Soc. 38(4) (2012), 925-934.
  25. Nieto, J. J. and López, R. R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, 223-239, (2005).
  26. Nieto, J. J. and López, R. R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sinica, Engl. Ser. 23 (12) (2007), 2205-2212.
  27. O'Regan, D. and Petrusel A.: Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl. 341 (2008), 1241-1252.
  28. Radenovic, S.: Remarks on some coupled coincidence point in partially ordered metric spaces. Arab Jour. Math. Sci., 20(1) (2014), 29-39.
  29. Radenovic, S.: A note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces. App. Math. Comp. 236 (2014), 367-372.
  30. Ran, A. C. M., Reurings, M. C. B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 132 (2004), 1435-1443.
  31. Roldán, A., Mart ´inez-Moreno, J. and Roldán, C.: Multidimensional fixed point theorems in partially ordered metric spaces. Journal of Mathematical Analysis and Applications, 396 (2012), 536-545.
  32. Roldán, A., Mart ´inez-Moreno, J., Roldán, C., Karapinar, E.: Multidimensional fixed-point theorems in partially ordered completely partial metric spaces under (φ,ψ)-contractivity conditions. Abst. Appl. Anal. 2013 (2013). Article ID 634371.
  33. Roldán, A., Mart ´inez-Moreno, J., Roldán, C., Cho, Y.J.: Multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces. Fuzzy Sets Syst. (2013).
  34. Samet, B., Vetro, C.: Coupled fixed point, f-invariant set and fixed point of N-order. Ann. Funct. Anal. 1 (2) (2010), 4656-4662.
  35. Samet, B., Vetro, C. and Vetro, F.: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013 (2013), Art. ID 5.
  36. Samet, B., Karapinar, E., Aydi, H. and Rajic, V. C.: Discussion on some coupled fixed point theorems. Fixed Point Theory Appl., 2013 (2013), Art. ID 50.
  37. Sharma, A., Imdad, M., Alam, A.: Shorter proofs of some recent even-tupled coincidence theorems for weak con- tractions in ordered metric spaces. Math. Sci., 8 (2014), 131-138.