Unique Common Fixed Points For Maps With ( ,, )- Contractive Condition In * W -Spaces

Year 2016, Volume: 29 Issue: 2, 413 - 417, 27.10.2016

K. P.R. Rao , K. V.Siva Parvathi K. R.K. Rao

Abstract

In this paper, we introduce $W^{*}$-spaces which generalizes $W$-spaces introduced by Piao and Jin \cite {PJ} and prove three unique common fixed point theorems in it. Some illustrative examples to highlight the results are furnished.

Keywords

$W^{*}$-spaces, Converse commuting maps, Common fixed points

References

• B.C.Dhage, A common fixed point principle inD-metric spaces, Bull.Cal. Math.Soc., 91, No.6(1999),475-480.
• B.C.Dhage, A.M.Pathan and B.E.Rhodes, A general existance principle for fixed point theorem in D-metric spaces, Int. J. Math. Math. Sci., 23(2000), 441-448.
• M.Aamri, D.E.Moutawakil , Some new common fixed points under strict contractive conditions, J.Math.Anal.Appl.,270,(2002),181-188.
• M.Aamri, D.E.Moutawakil , Common fixed points under contractive conditions in symmetric spaces, J.Applied Mathematics E-Notes, 3,(2003),156-162.
• S.G. Matthews, Partial metric topology, Proc. 8th Summer conference on General Topology and Applications, Ann. New York Acad. Sci., vol. 728, 1994, 183 - 197.
• Sh.Sedghi, N.Shobe and H.Zhou, A common fixed point theorem in D-metric spaces, Fixed point * theory and Applications ,vol. 2007 (2007), Artical Id 27906, 13 pages.
• Sh.Sedghi, K.P.R.Rao and N.Shobe, Common fixed point theorems for six weakly compatible mappings in D-metric spaces, Int. J. Math. Math. Soc., Vol. * 6, (2), (2007), 225-237.
• T.Abdeljawad, E. Karapinar and K.Tas, Existence and uniqueness of a common fixed point on partial metric sapces Appl.Math.Lett., vol.24 (11), (2011), 1900 - 1904.
• T.L.Hicks , B.E.Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, J.Nonlinear Analysis, 36,(1993),331-334.
• Y.J. Piao and Y.X. Jin, Unique common fixed points for maps satisfying contractive conditions on W-spaces, J. Sys. Sci. and Math. Scis., 5(2012), 601-609.
• Z. Lin, Oncommon fixed point for converse commuting self maps on metric spaces, Acta Anal. Funct. Appl., 4(3), (2012), 266-228.
• Z.Mustafa, B.Sims, A new approach to generalized metric spaces. J Nonlinear Convex Anal, 7(2),(2006), 289-297.
• Z.Mustafa, B.Sims, Fixed point theorems for contractive mapping in complete G-metric spaces. Fixed point Theory Appl, 2009, (2009),Article ID 917175, 10 pages