Fixed Point Theorems for Cyclic Weak Φ – Contraction in Menger Space
Sahni Mary Roosevelt , K. S. Dersanambika. "Fixed Point Theorems for Cyclic Weak Φ – Contraction in Menger Space", International Journal of Mathematical Trends and Technology (IJMTT). V8:154-156 April 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.
Abstract
Cyclic weak ϕ-contraction mapping is introduced in Menger space and fixed point theorem for such mappings are studied in Menger space.
References
[1] D. Gopal, M.Imdad, M.Hasan: Fixed point theorems for cyclic weak ϕ-contraction in Fuzzy metric spaces, Journal of nonlinear analysis and application, 2012, pp1-11.
[2] E. Karapinar, A.Yildiz, I.M,Erhan: Cyclic contractions on G-metric spaces, Hindawi publishing cooperation, 2012, pp 1-15.
[3] E. Karapinar, Fixed point theory for cyclic weak ϕ -contraction, Applied Mathematics letters, vol 24 , 2011, pp 822-825.
[4] H. K. Nashine, W. S. P. Kumam : Cyclic generalized contractions and fixed point results with applications to an integral equation, 2012, pp 217.
[5] K.Jha, M. Abbas, I. Beg, R.P. Pant, M. Imdad: Common fixed point theorem for (ϕ, ψ ) weak contraction in fuzzy metric spaces, Bulletin of Mathematical analysis and applications, vol 3, 2011, pp 149-158.
[6] M. Pacurar, Ioan A. Rus: Fixed point theory for cyclic ϕ -contractions, Nonlinear Analysis, vol 72 , 2010, pp 1181-1187.
[7] S. Chauhan, S. Bhatt, N. Dhiman: Some fixed point results in Menger spaces, Advances in fixed point theory, vol 2 , 2012, pp 452-463.
Keywords
Menger space, cyclic representation, cyclic weak ϕ – contraction.