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2010, vol. 14, iss. 2, pp. 125-143
New solutions of Peano's differential equation
University of Belgrade, Faculty of Mathematics

emailandreja@predrag.us
Abstract
This paper gives sufficient conditions for new solutions of Peano's differential equation in the class of all lower continuous mappings. In this sense, this paper presents new fixed point theorems of Schauder type on lower transversal spaces. For the lower transversal space (X; ρ) are essential the mappings T : X → X which are un- bounded variation, i.e., if Σρ(Tnx, Tn+1x)=+∞ for arbitrary x Є X. On the other hand, for upper transversal spaces are essential the mappings T : X → X which are bounded variation.
References
Peano, G. (1890) Démonstration de lintegrabilite des équations différentielles ordinaires. Math. Ann, 37, 182{228
Tasković, M.R. (1985) A characterization of the class of contraction type mappings. Kobe J. Math, 2, 45-55
Tasković, M.R. (1998) Transversal spaces. Mathematica Moravica, 2, 133-142
Tasković, M.R. (2001) Nonlinear functional analysis. in: Second Book: Monographs - Global Convex Analysis - General convexity, Variational methods and Optimization, Beograd: Zavod za udžbenike i nastavna sredstva, in Serbian
Tasković, M.R. (2003) Transversal intervally spaces. Mathematica Moravica, br. 7, str. 91-106
Tasković, M.R. (2003) Survey on transversal normed spaces. Mathematica Moravica, br. 7, str. 153-174
Tasković, M.R. (2003) Fixed points on transversal edges spaces. Mathematica Moravica, br. 7, str. 175-186
Tasković, M.R. (2002) On Schauder's 54th problem in scottish book revisited. Mathematica Moravica, br. 6, str. 119-126
Tasković, M.R. (2004) Theory of transversal point, spaces and forks. in: Monographs of a new mathematical theory, Beograd, 1000 pages, In Serbian, to appear
 

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article language: English
document type: unclassified
DOI: 10.5937/MatMor1002125T
published in SCIndeks: 15/03/2011

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