EN
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
- 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.
- S. Banach. Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fund. Math., 3:133-181, 1922.
- 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.
- H. G. Barone. Limit points of sequences and their transforms by methods of summability. Duke Math. J., 5:740-752, 1939.
- A. Bollenbacher and T.L.Hicks. A xed point theorem revisited. Proc. Amer. Math. Soc., 102:898-900, 1988.
- D. W. Boyd and J. S. W. Wong. Another proof of contraction mapping theorem. Canad. Math. Bull., 11:605-606, 1968.
- D. W. Boyd and J. S. W. Wong. On nonlinear contractions. Proc. Amer. Math. Soc., 20:458-464, 1969.
- 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