Abstract
A fixed point theorem for nonlinear contraction in the modular space is proved. Moreover, a fixed point theorem for asymptotic contraction in this space is studied.
A fixed point theorem for nonlinear contraction in the modular space is proved. Moreover, a fixed point theorem for asymptotic contraction in this space is studied.
H. Nakano, Modular Semi-Ordered Spaces, Tokyo, Japan, 1959.
J. Musielak and W. Orlicz, “On modular spaces,” Studia Mathematica, vol. 18, pp. 49–65, 1959.
View at: Google Scholar | Zentralblatt MATH | MathSciNetT. Dominguez Benavides, M. A. Khamsi, and S. Samadi, “Uniformly Lipschitzian mappings in modular function spaces,” Nonlinear Analysis, vol. 46, no. 2, Ser. A: Theory Methods, pp. 267–278, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Hajji and E. Hanebaly, “Fixed point theorem and its application to perturbed integral equations in modular function spaces,” Electronic Journal of Differential Equations, vol. 2005, no. 105, pp. 1–11, 2005.
View at: Google Scholar | MathSciNetE. Hanebaly, “Fixed point theorems in modular space,” November 2005, http://arxiv.org/abs/math.FA/0511319v1.
View at: Google ScholarM. A. Khamsi, “Nonlinear semigroups in modular function spaces,” Mathematica Japonica, vol. 37, no. 2, pp. 291–299, 1992.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical Society, vol. 20, no. 2, pp. 458–464, 1969.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetI. D. Arandelović, “On a fixed point theorem of Kirk,” Journal of Mathematical Analysis and Applications, vol. 301, no. 2, pp. 384–385, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Edelstein, “On fixed and periodic points under contractive mappings,” Journal of the London Mathematical Society, vol. 37, no. 1, pp. 74–79, 1962.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetL. B. Ćirić, “A generalization of Banach's contraction principle,” Proceedings of the American Mathematical Society, vol. 45, no. 2, pp. 267–273, 1974.
View at: Google Scholar | Zentralblatt MATH | MathSciNetE. Rakotch, “A note on contractive mappings,” Proceedings of the American Mathematical Society, vol. 13, no. 3, pp. 459–465, 1962.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Reich, “Fixed points of contractive functions,” Bollettino dell'Unione Matematica Italiana (4), vol. 5, pp. 26–42, 1972.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. A. Kirk, “Contraction mappings and extensions,” in Handbook of Metric Fixed Point Theory, W. A. Kirk and B. Sims, Eds., pp. 1–34, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Ait Taleb and E. Hanebaly, “A fixed point theorem and its application to integral equations in modular function spaces,” Proceedings of the American Mathematical Society, vol. 128, no. 2, pp. 419–426, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. Caccioppoli, “Una teorem general sull'esistenza di elementi uniti in una transformazione funzionale,” Rendiconti dell'Accademia Nazionale dei Lincei, vol. 11, pp. 794–799, 1930.
View at: Google ScholarF. E. Browder, “Nonlinear operators and nonlinear equations of evolution in Banach spaces,” in Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968), pp. 1–308, American Mathematical Society, Providence, RI, USA, 1976.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY.-Z. Chen, “Asymptotic fixed points for nonlinear contractions,” Fixed Point Theory and Applications, vol. 2005, no. 2, pp. 213–217, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Gerhardy, “A quantitative version of Kirk's fixed point theorem for asymptotic contractions,” Journal of Mathematical Analysis and Applications, vol. 316, no. 1, pp. 339–345, 2006.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Jachymski and I. Jóźwik, “On Kirk's asymptotic contractions,” Journal of Mathematical Analysis and Applications, vol. 300, no. 1, pp. 147–159, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetW. A. Kirk, “Fixed points of asymptotic contractions,” Journal of Mathematical Analysis and Applications, vol. 277, no. 2, pp. 645–650, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetT. Suzuki, “Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces,” Nonlinear Analysis, vol. 64, no. 5, pp. 971–978, 2006.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH.-K. Xu, “Asymptotic and weakly asymptotic contractions,” Indian Journal of Pure and Applied Mathematics, vol. 36, no. 3, pp. 145–150, 2005.
View at: Google Scholar | Zentralblatt MATH | MathSciNet