On Some New Contractive Conditions for Asymptotically Regular Set-Valued Mappings

Article Sidebar

PDF
Cite as:
Pradip Debnath, Manuel de La Sen, On Some New Contractive Conditions for Asymptotically Regular Set-Valued Mappings, Int. J. Anal. Appl., 18 (4) (2020), 586-593.

Main Article Content

Pradip Debnath, Manuel de La Sen

Abstract

In this paper, we introduce two new contractive conditions of Proinov-type for asymptotically regular set-valued mappings and prove the existence of their fixed points. Our results extend some results due to Nadler and Boyd and Wong.

Article Details

References

  1. J. P. Aubin and J. Siegel. Fixed points and stationary points of dissipative multivalued maps. Proc. Amer. Math. Soc., 78 (1980), 391-398.
  2. I. Beg and A. Azam. Fixed points of asymptotically regular multivalued mappings. J. Austral. Math. Soc. (Series A), 53 (1992), 284-289.
  3. M. Berinde and V. Berinde. On a general class of multi-valued weakly picard mappings. J. Math. Anal. Appl., 326 (2007), 772-782.
  4. M. Boriceanu, A. Petrusel, and I.A. Rus. Fixed point theorems for some multivalued generalized contraction in b-metric spaces. Int. J. Math. Stat., 6 (2010), 65-76.
  5. D. W. Boyd and J. S. Wong. On nonlinear contractions. Proc. Amer. Math. Soc., 20 (1969), 458-464.
  6. F. E. Browder and W. V. Petryshyn. The solution by iteration of nonlinear functional equation in Banach spaces. Bull Am. Math. Soc., 72 (1966), 571-576.
  7. S. Czerwik. Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem. Mat. Univ. Modena, 46 (1998), 263-276.
  8. P. Z. Daffer and H. Kaneko. Fixed points of generalized contractive multi-valued mappings. J. Math. Anal. Appl., 192 (1995), 655-666.
  9. P. Debnath and M. de La Sen. Contractive inequalities for some asymptotically regular set-valued mappings and their fixed points. Symmetry, 12 (2020), 411.
  10. P. Debnath and M. de La Sen. Fixed points of eventually δ-restrictive and δ( )-restrictive set-valued maps in metric spaces. Symmetry, 12 (2020), 127.
  11. H. W. Engl. Weak convergence of asymptotically regular sequences for nonexpansive mappings and connections with certain Chebyshef-centers. Nonlinear Anal., Theory Methods Appl., 1 (5) (1977), 495-501.
  12. M. D. Guay and K. L. Singh. Fixed points of asymptotically regular mappings. Math. Vesnik, 35 (1983), 101-106.
  13. S. Itoh and W. Takahashi. Single valued mappings, multivaluued mappings and fixed point theorems. J. Math. Anal. Appl., 59 (1977), 514-521.
  14. S. B. Nadler. Multi-valued contraction mappings. Pac. J. Math., 30 (2) (1969), 475-488.
  15. P. D. Proinov. Fixed point theorems for generalized contractive mappings in metric spaces. J. Fixed Point Theory Appl., 22 (2020), 21.
  16. B. E. Rhoades. A comparison of various definitions of contractive mappings. Trans. Amer. Math. Soc., 226 (1977), 257-290.
  17. B. E. Rhoades, S. Sessa, M. S. Khan, and M. Swaleh. On fixed points of asymptotically regular mappings. J. Austral. Math. Soc. (Ser. A), 43 (1987), 328-346.
  18. B. E. Rhoades, S. L. Singh, and C. Kulshrestha. Coincidence theorem for some multivalued mappings. Int. J. Math. and Math. Sci., 7 (3) (1984), 429-434.
  19. S. L. Singh, S. N. Mishra, and R. Pant. New fixed point theorems for asymptotically regular multi-valued maps. Nonlinear Anal., Theory Methods Appl., 71 (2009), 3299-3304.