Teorema Titik Tetap Fungsi Demicontinuous Hampir Lipschitzian di Ruang Hilbert

Authors

  • Muhamad Najibufahmi Program Studi Pendidikan Matematika FKIP UNIKAL
  • Nurul Aini Program Studi Pendidikan Matematika FKIP UNIKAL

DOI:

https://doi.org/10.31941/delta.v2i1.466

Keywords:

Titik tetap, ruang Hilbert, fungsi hampir Lipschitzian, demicontinuous

Abstract

Tujuan paper ini adalah membangun teorema titik tetap untuk fungsi hampir Lipschitzian di ruang Hilbert dengan menggunakan ide pembuktian yang berbeda dibandingkan dengan Sahu (2005). Diberikan U himpunan bagian dari ruang Hilbert H dan

References

Banach, S., 1992, Sur less operations donsles ensembes abstraits et leurs applications, Fund. Math. 3, pp. 133 - 181.

Browder, F.E., 1965, Fixed point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53, pp. 1272 - 1276.

Bruck, R., Kuczumov, dan T., Reich, S., 1993, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloqium Mathematicum, 65, pp. 169 -179.

Byrne, C., 2004, A unified treatment of some iterative algorithms in signal processing and image construction, Inverse Probl., 20, pp. 103 - 120.

Combettes, P.L., 1996, The convex feasibility problem in image recovery, [in:] Advances in Imaging and Electron Physics, 95, pp. 195 -270.

Dung, L.A. dan Tan, D.H., 2003, Fixed points of semigroups of Lipschitzian mappings, Acta Math. Viet. 28, pp. 89 - 100.

Ishihara, H., 1989, Fixed point theorems for Lipschitzian semigroups, Canad. Math. Bull., 32, pp. 90 - 97.

Ishihara, H. dan Takahashi, W., 1987, Fixed point theorems for uniformly Lipschitzian semigroups in Hilbert spaces, J. Math. Anal. Appl. 127, pp. 206 - 210.

Kirk, W.A., 1974, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., pp. 339 - 346.

Kitahara, S. dan Takahashi, W., 1993,Image recovery by convex combinations of sunny non-expansive retractions, Topol. Methods Nonlinear Anal., 2, pp. 333 - 342.

Kreyszig, E., 1978, Introductory Functional Analysis with Applications, John Wileys & Sons, New York.

Lim, T.C., 1980, On asymptotic centers and fixed points of nonexpansive mappings, Canadian J. Math., 32, pp. 421 - 430.

Sahu, D.R., 2005, Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces, Comment. Math. Univ. Carolinae, 46, pp. 653 - 666.

Suathai, S. dan Puengrattana, W., 2014, Fixed point theorems for a semigroup of total asymptotically nonexpansive mappings in uniformly convex Banach spaces, Opuscula Math. 34, pp. 183 - 197.

Weissinger, J., 1952, Sur theorie and anwendung des interationsvertahrens, Math. Nachr., 8, pp. 193 - 212.

Yang, C., A new fixed point theorem for non-expansive mappings and its applications, arXiv:1208.0979v1 [math.FA], 5 Aug 2012.

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Published

2017-08-18