Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces

Year 2014, Volume: 27 Issue: 1, 653 - 658, 28.03.2014

Shaban Sedghı , Nabi Shobkolaeı , S. Fırouzıan

Abstract

In this paper, we apply the concept of cyclic(φ ) -contraction for presenting a fixed point theorem on Hausdorff uniform space. Some more general results are also obtained in Hausdorff uniform space.

Keywords

Fixed point, Uniform Space, Cyclic (φ ) -contraction.

References

• Aamri, M., Bennani, S., El Moutawakil, D., “Fixed points and variational principle in uniform spaces”, Siberian Electronic Mathematical Reports, 3: 137– 142 (2006).
• Aamri, M., El Moutawakil, D., “Common Fixed Point Theorems for E-contractive or E-expansive Maps in Uniform Spaces”, Acta Math. Acad. Paedagog. Nyh´azi (N.S.), 20(1): 83-91(2004).
• Berinde, V., “Iterative Approximation of Fixed Points”, Editura Efemeride, Baia Mare, (2002).
• Berinde, V., “Contractii Generalizate si Aplicatii”, vol. 22, Editura Cub Press, Baia Mare, (1997).
• Bourbaki, N., “´E l´ements de math´ematique. Fasc. II. Livre III: Topologie g´en´erale. Chapitre 1: Structures topologiques. Chapitre 2: Structures uni- formes”, Scientifiques et Industrielles, No. 1142, Hermann, Paris, (1965). ´edition., Actualit´es
• Jachymski, J., “Fixed Point Theorems for Expansive Mappings”, Math. Japon., 42(1):131-136(1995).
• Kada, O., Suzuki, T., Takahashi, W., “Nonconvex Minimization Theorems and Fixed Point Theorems in Complete Metric Spaces”, Math. Japon., 44(2): 381-391(1996).
• Karapnar, E., “Fixed point theory for cyclic weak φ-contraction”, Appl.Math. Lett., 24(6): 822-825 (2011).
• Karap nar, E., Sadarangani, K., “Fixed point theory for cyclic (φ−
• ψ)-contractions”, Fixed Point Theory
• 1186/1687-1812-2011-69. 69, (2011) doi:
• Kirk, W.A., Srinivasan, P.S., Veeramani, P., “Fixed points for mappings satisfying cyclical weak contractive conditions”, Fixed Point Theory, 4(1): 79–89(2003).
• Pacurar, M., Rus, I.A., “Fixed point theory for cyclic ϕ-contractions”, Nonlinear Amal., 72: 1181- 1187(2010).
• Rhoades, B.E., “A Comparison of Various Definitions of Contractive Mappings”, Trans. Amer. Math. Soc., 226: 257-290 (1977). [13] Rus, I.A., “Generalized Contractions and Applications”, Cluj University Press, Cluj-Napoca, (2001).
• Rus, I.A., “Cyclic representations and fixed points”, Ann. T. Popoviciu, Seminar Funct. Eq. Approx. Convexity, 3: 171-178(2005).
• De La Sen, M., “Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings”, Applications, Article ID 572057(2010). Point Theory and
• Wang, S.Z., Li, B. Y., Gao, Z. M., Is´eki, K., “Some Fixed Point Theorems on Expansion Mappings”, Math. Japon., 29(4): 631-636(1984).
• Zeidler, E., “Nonlinear Functional Analysis and its Applications”, Vol. 1, Springer- Verlag, New York, (1986).