Fixed Points of Expansive Type Mappings in 2-Banach Spaces

Main Article Content

Prabha Chouhan, Neeraj Malviya

Abstract

In present paper, we define expansive mappings in 2-Banach space and prove some common unique fixed point theorems which are the extension of results of Wang et al. [12] and Rhoades [9] in 2-Banach space.

Article Details

References

  1. Cho Y.J. Khan M.S. and Sing S.L. Common fixed points of weakly commuting mappings, Univ.u. Novom Sadu, Zb.Rad. Period.-Mat.Fak.Ser.Mat, 18 1(1988)129-142.
  2. Gahler S. 2-metric Raume and ihre topologische strucktur, Math.Nachr., 26(1963), 115-148.
  3. Gahler S. Uber die unifromisieberkeit 2-metrischer Raume, Math.Nachr. 28(1965), 235 - 244.
  4. Iseki K. Fixed point theorems in 2-metric space, Math.Seminar.Notes, Kobe Univ.,3(1975), 133 - 136.
  5. Jungck G., Commuting mappings and fixed points The American Mathematical Monthly, Vol.83, no.4,PP.261-263, 1976.
  6. Machuca R., A coincidence theorem The American Mathematical Monthly, Vol.74, no.5,P. 569, 1967.
  7. Panja C. and Baisnab A.P., Asymptotic regularity and fixed point theorems, The Mathematics Student, 46 1(1978), 54-59.
  8. Rhoades B.E. Contractive type mappings on a 2-metric space, Math.Nachr., 91(1979), 151- 155.
  9. Rhoades B.E., Some fixed point theorems for pairs of mappings, Jnanabha 15 (1985), 151-156.
  10. Rhoades B.E., A comparison of various definitions of contractive mappings. Tran. Am. Math.Soc.226, 257-290 (1977)
  11. Saha M. Dey D. Ganguly A. and Debnath L. Asymptotic regularity and fixed point theorems on a 2-Banach space Surveys in Mathematics and its Applications Vol.7(2012), 31-38.
  12. Wang S. Z., Li B. Y., Gao Z. M., and Iseki K., Some fixed point theorems on expansion mappings, Math. Japonica 29 (1984), 631-636.
  13. White A. 2-Banach spaces, Math.Nachr., 42(1969), 43 - 60.
  14. Zhang S., Fixed point theory and its applications, Chongqing press, Chongqing China, 1984.