Fixed points in modular spaces with new type contractivity


  • Tayebe Lal Shateri Hakim Sabzevari University





Fixed point, contraction, modular, modular space.


In this present paper, we prove a common _xed point theorem for self maps in modular spaces. Also one corollary, which shows that our main theorem is generalized version of the main theorem of [A. Razani, E. Nabizadeh, M.Beyg Mohamadi and S. Homaei Pour, Abs. Appl. Anal. 2007, Article ID 40575] is given.


H. Nakano, Modulared Semi-Ordered Linear Spaces, Tokyo Math. Book Ser., Vol. 1, Maruzen Co., Tokyo, 1950.

J. Musielak and W. Orlicz, "On Modular Spaces", Studia Math., Vol. 18, (1959), pp.49-56.

S. Koshi, T. Shimogaki, "On F{norms of quasi{modular spaces", J. Fac. Sci. Hokkaido Univ. Ser. I, Vol. 15, No. 3, (1961), pp.202-218.

S. Yamamuro, "On conjugate spaces of Nakano spaces", Trans. Amer. Math. Soc., Vol. 90, (1959), pp.291-311.

M.A. Krasnoselskii and Y.B. Rutickii, "Convex functions and Orlicz spaces", Fizmatgiz, Moskva [In Russian; English translation, Noordho_, Groningen], (1961).

W.M. Koslowski, Modular function spaces, Dekker: New York, Basel, (1988).

J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. Vol. 1034 , Springer-verlag, Berlin, 1983.

I.D. Arandelovi_c, "on a fixed point theorem of Kirk", J. Math. Anal. Appl., Vol.301, No. 2, (2005), pp.384-385.

M. Edelstein, "On fixed and periodic points under contractive mappings", J. London Math. Soc., Vol. 37, No. 1, (1962), pp.74-79.

L.B _ Ciri_c, "A generalization of Banach's contraction principle", Proc. Amer. Math. Soc., 45(2) (1974), pp.267-273.

E. Rakotch, "A note on contractive mappings", Proc. Amer. Math. Soc., Vol. 13, No. 3, (1962), pp.459-465.

S. Reich, "Fixed points of contractive functions", Bollettino dell'Unione Mathematica Italiana, Vol. 4, No. 5, (1972), pp. 26-42.

W.A. Kirk, contraction mappings and extensions, Handbook of Metric Fixed Point Theory, W.A. Kirk and B. Sims, Eds. Kluwer Academic Publishers, Dordrecht, The Netherlands, (2001), pp.1-34.

A. Razani, E. Nabizadeh, M. Beyg Mohamadi and S. Homaei Pour, "Fixed points of nonlinear and asymptotic contraction in modular spaces", Abs. Appl. Anal., Vol. 2007, (2007), Article ID 40575, 10 pages.

M. A. Khamsi, "Quasicontraction Mapping in modular spaces without _2-condition", Fixed Point Theory and Applications, Vol. 2008, (2008), Artical ID 916187, 6 pages.

K. Kuaket and P. Kumam, "Fixed point of asymptotic pointwise contractions in modular spaces", Appl. Math. Letters, Vol. 24, (2011), pp.1795-1798.

X. Wang and Y. Chen, "Fixed points of asymptotic pointwise nonexpansive mappings in modular spaces", J. Appl. Math., Vol. 2012, (2012), Article ID 319394, 6 pages.

I. Alton, M. Abbas and H. Simsek, "A _xed point theorem on cone metric spaces with new type contractivity", Banach J. Math. Anal., Vol. 5, No. 2, (2011), pp.15-24.

View Full Article: