This book is devoted to metric fixed point theory. The goal is to develop, in a self-contained fashion, those results in this theory which involve the use of measures of noncompactness. Some of the well-known fixed point theorems are included with several applications to the theory of differential equations.This book is mainly addressed to graduate students who wish to learn about metric fixed point theory, but it will also be useful to researchers in the area.Most of the results presented here were obtained by the authors over the last ten years and have not previously appeared in any other textbook.
M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo. This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory.
M. Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Several topics in these notes can be found either in texts on measures of noncompactness (see ) or in books on metric fixed point theory (see,, ).
Authors: Ayerbe Toledano, . Measures of Noncompactness. Minimal Sets for a Measure of Noncompactness. Dominguez Benavides, Tomas, López-Acedo, Genaro. Toledano, J. M. Ayerbe (et a.
Measures of Noncompactness in Metric Fixed Point Theory. Measures of Noncompactness in Metric Fixed Point Theory. Ayerbe Toledano, Tomas Dominguez Benavides, G. Lopez Acedo. Download (pdf, . 2 Mb) Donate Read.
Fixed Point Theory has two main branches: on the one hand we can consider the . Tomás Domínguez Benavides Measures of Noncompactness in Metric Fixed Point Theory.
Fixed Point Theory has two main branches: on the one hand we can consider the results that are deduced from topological properties and on the other hand those which can be obtained using metric properties. Do you want to read the rest of this article? Request full-text. Tomás Domínguez Benavides. We prove that for every Banach space which can be embedded in c0(Γ) (for instance, reflexive spaces or more generally spaces with M-basis) there exists an equivalent renorming which enjoys the (weak) Fixed Point Property for non-expansive mappings.
Hausdorff measure of non-compactness and Darbo-Sadovskii fixed point theorem are employed to deal with the non-Lipschitz case. Common Fixed Point Theorems for Compatible and Weakly Compatible Maps in G-Metric Spaces. Asha Rani, Sanjay Kumar, Naresh Kumar, S. K. Garg. 310166 4 614 Downloads 7 526 Views Citations. JMA Toledano, TD Benavides, GL Acedo. Random fixed points of set-valued operators. T Benavides, G Acedo, HK Xu. Proceedings of the American Mathematical Society 124 (3), 831-838, 1996. Springer Science & Business Media, 1997. JM Ayerbe Toledano, T Dominguez Benavides, G López Acedo. Theory Adv. Appl 99, 1997. Some Properties of the Set and Ball Measures of NonCompactness and Applications. Journal of the London Mathematical Society 2 (1), 120-128, 1986.
References J. Domı́nguez Benavides, and G. López Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Operator Theory: Advances and Applications, vol. 99, Birkhäuser, Basel, 1997. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1974. T. Domı́nguez Benavides, G. López Acedo, and . Xu, Random fixed points of set-valued operators, Proceedings of the American Mathematical Society 124 (1996), no. 3, 831–838.
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