Some Results In The Fixed Point Theory II
Milan R. Tasković (1980)
Publications de l'Institut Mathématique
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Milan R. Tasković (1980)
Publications de l'Institut Mathématique
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Solomon Leader, Stephen Hoyle (1975)
Fundamenta Mathematicae
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C. Badea (2002)
Studia Mathematica
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Let T and V be two Hilbert space contractions and let X be a linear bounded operator. It was proved by C. Foiaş and J. P. Williams that in certain cases the operator block matrix R(X;T,V) (equation (1.1) below) is similar to a contraction if and only if the commutator equation X = TZ-ZV has a bounded solution Z. We characterize here the similarity to contractions of some operator matrices R(X;T,V) in terms of growth conditions or of perturbations of R(0;T,V) = T ⊕ V.
Lj.B. Ciric (1972)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Berthold Schweizer, Howard Sherwood, Robert M. Tardiff (1988)
Stochastica
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The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,t) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger...
Kubrusly, C.S., Levan, N. (2001)
International Journal of Mathematics and Mathematical Sciences
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Ovidiu Popescu (2009)
Open Mathematics
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In this paper we prove two fixed point theorems for generalized contractions with constants in complete metric space, which are generalizations of very recent results of Kikkawa and Suzuki.
P. L. Sharma, A. K. Yuel (1982)
Matematički Vesnik
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Memudu Olatinwo (2008)
Open Mathematics
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In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results...
Santanu Dey (2012)
Colloquium Mathematicae
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We identify how the standard commuting dilation of the maximal commuting piece of any row contraction, especially on a finite-dimensional Hilbert space, is associated to the minimal isometric dilation of the row contraction. Using the concept of standard commuting dilation it is also shown that if liftings of row contractions are on finite-dimensional Hilbert spaces, then there are strong restrictions on properties of the liftings.
Abbas, M., Rhoades, B.E. (2008)
Fixed Point Theory and Applications [electronic only]
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Simeon Reich, Alexander J. Zaslavski (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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We establish two fixed point theorems for certain mappings of contractive type.