Common Fixed Point Theorems for Co-Cyclic Weak Contractions in Compact Metric

Authors: Alemayehu Geremew Negash

Abstract:

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.

Keywords: Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337085

References:

[1] M. Akkouchi and V. Popa, Well-posedness of fixed point problem for three mappings under strict contractive conditions, Bull. Math. Inform. Physics, Petroleum-Gash Univ. Ploiesti, 61 (2) (2009) 1–10
[2] Ya. I. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New Results in operator theory, Advanced and Appl. (Ed. by I. Gohberg, Yu,Lyubich), Birkhauser Verlag, Besel , 98 (1997) 7–22
[3] G.V.R. Babu and G.N. Alemayehu, A common fixed point theorem for weakly contractive mappings satisfying property (E. A), Applied Mathematics E-Notes, 10 (2010) 167–174.
[4] I. Beg and M. Abbas, Coincidence points and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed point theory and applications, 2008, ID. 74503, 1–7.
[5] P. Chaipunya, Y. J. Cho, W. Sintunavarat, P. Kumam, Fixed point and common fixed point theorems for cyclic Quasi-contractions in Metric and Ultrametric spaces, Advances in Pure Mathematics, 2 (2012) 401–407.
[6] J. Harjani, B. Lopez, K. Sadarangani, Fixed ppoint theorems for cyclic weak contractions in compact metric spaces, J. Nonlinear Analysis, 6 (2013) 279–284.
[7] G. Jungck and B.E. Rhoades, Fixed points for set valued functions with out continuity, Indian J. Pure. Appl. Math., 29 (3)(1998) 227-238.
[8] E. Karapinar, Fixed point theory for cyclic ϕ-contraction, Appl. Math. Lett., 24 (2011) 822–825.
[9] W.A. Kirk, P.S. Srinavasan, P. Veeramani, Fixed Points for mapping satisfying cylical contractive conditions, Fixed Point Theory 4 (2003), 7989
[10] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis 47 (2001) 2683–2693.
[11] I. A. Rus, Cyclic Representation and fixed points, Ann. T. Popoviciu Seminar Func. Eq. Approx. Convexity, 3 (2005) 171–178.