Common fixed point theorems for uniformly subcompatible mappings satisfying more general condition

Authors

  • R. Sumitra Department ofMathematics, SMK Fomra Institute of Technology, Chennai-603 103, Tamilnadu, India.
  • V. Rhymend Uthariaraj Ramanujan Computing Centre, Anna University, Chennai-600 025, Tamilnadu, India.
  • P. Vijayaraju Department ofMathematics, Anna University, Chennai-600 025, Tamilnadu, India
  • R Hemavathy Anna University

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.493

Keywords:

uniformly subcompatible mappings, generalized ciric type contractive condition, gregus type condition, common fixed point, best approximation, Locally convex space.

Abstract

We prove common fixed point theorems for uniformly subcompatible mappings satisfying a more generalized ciric type condition and a condition more general than gregus type condition in a locally convex domain. As an application, we have also established best  approximation result. Our results extend recent results existing in the literature.

References

F. Akbar and A. R. Khan, Common fixed point and approximation results for noncommuting maps on locally convex spaces, Fixed point theory and applications, 2009(2009), article ID 207503, pp.14 pages.

S. Al-Mezel and N. Hussain, On common fixed point and approximation results of gregus type, Int. Math. Forum, 2 (2007), 1839–1847.

G. V. R. Babu and K. N. V. V. Prasad, Common fixed point theorems of diRerent compatible type mappings Ciric’s contraction type condition, Mathematical Communications, 11(2006), 87–102.

Lj. B. Ciric, On a common fixed point theoremof a Gregus type, Publ. Inst.Math., 49(1991), 174–178. COMMON FIXED POINT THEOREMS 17

B. Fisher and S. Sessa, On a fixed point theorem of Gregus, Int. J.Math.Math. Sci., 9(1986), 23–28.

M. Gregus, Jr., A fixed point theoremin Banach space, Bull. UnMat. Ital., 5(1980), 193–198.

G. Jungck, Compatible mappings and common fixed points, Internat. J.Math.Math. Sci., 9(1986), 43–49.

G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proceedings of the American Mathematical Soceity, 103(1988), 977–983.

N. Hussain and A. R. Khan, Common fixed point results in best approximation theory, Applied Mathematics Letters, 16(2003), 575–580.

A. R. Khan, F. Akbar and N. Sultana, Random coincidence points of subcompatible multivalued maps with applications, Carpathian Journal ofMathematics, 24(2008), 63–71.

G. Kothe, Topological Vector Spaces, Springer verlag, New York, 1969.

M. A. Kutbi,On common solution of contractive -typemaps, Int. J. ContemporaryMath. Sci., 4(2009), 541 -548.

R. N.Mukherjee and V. Verma, A note on fixed point theorem of gregus, Math. Japon., 33(1988), 745–749.

H. K. Nashine andM. S. Khan, An application of fixed point theorem to best approximation in locally convex space, Appl.Math. Letters, in press 2009.

S. Reich, Approximate selections, best approximations, fixed point and invariant sets, J. Math. Anal. Appl., 62(1978), 104-113.

S. P. Singh, Some results on best approximationin locally convex spaces, J. Approx. Theory., 28(1980), 329 -332.

E. Tarafdar, Some fixed point theorems on locally convex linar topological spaces, Bull. Austral.Math. Soc., 13 (1975), 241–254.

P. Vijayaraju, Fixed point theorems for asymptotically nonexpansive mapping, Bull. Calcutta Math. Soc., 80(1998), 133–136.

Downloads

Published

2011-03-22

How to Cite

Sumitra, R., Uthariaraj, V. R., Vijayaraju, P., & Hemavathy, R. (2011). Common fixed point theorems for uniformly subcompatible mappings satisfying more general condition. Tamkang Journal of Mathematics, 42(1), 9–17. https://doi.org/10.5556/j.tkjm.42.2011.493

Issue

Section

Papers