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Some results in metric fixed point theory

Cilt: 1 Sayı: 2 20 Aralık 2017
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Some results in metric fixed point theory

Abstract

This is a survey of results mainly in metric fixed point theory, including the Darbo–Sadovski˘i theorem using measures of noncompactness. Various different proofs are presented for some of the most important historical results. Furthermore many examples and remarks are added to illustrate the topics of the paper.

Keywords

Kaynakça

  1. R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, and B. N. Sadovskii. Measures of Noncompactness and Condensing Operators. Birkha¨user Verlag, Basel, 1992.
  2. S. Banach. Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fund. Math., 3:133-181, 1922.
  3. J. Banas and K. Goebel. Measures of Noncompactness in Banach Spaces, volume 60 of Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, New York and Basel, 1980.
  4. H. G. Barone. Limit points of sequences and their transforms by methods of summability. Duke Math. J., 5:740-752, 1939.
  5. A. Bollenbacher and T.L.Hicks. A xed point theorem revisited. Proc. Amer. Math. Soc., 102:898-900, 1988.
  6. D. W. Boyd and J. S. W. Wong. Another proof of contraction mapping theorem. Canad. Math. Bull., 11:605-606, 1968.
  7. D. W. Boyd and J. S. W. Wong. On nonlinear contractions. Proc. Amer. Math. Soc., 20:458-464, 1969.
  8. H. Brezis and F. E. Browder. A general principle on ordered sets in nonlinear functional analysis. Advances in Mathematics, 21:355-364, 1976.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

20 Aralık 2017

Gönderilme Tarihi

30 Eylül 2017

Kabul Tarihi

28 Kasım 2017

Yayımlandığı Sayı

Yıl 2017 Cilt: 1 Sayı: 2

Kaynak Göster