Displaying similar documents to “A differential inclusion : the case of an isotropic set”

Global behavior of a third order rational difference equation

Raafat Abo-Zeid (2014)

Mathematica Bohemica

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In this paper, we determine the forbidden set and give an explicit formula for the solutions of the difference equation x n + 1 = a x n x n - 1 - b x n + c x n - 2 , n ∈ ℕ 0 where a , b , c are positive real numbers and the initial conditions x - 2 , x - 1 , x 0 are real numbers. We show that every admissible solution of that equation converges to zero if either a < c or a > c with ( a - c ) / b < 1 . When a > c with ( a - c ) / b > 1 , we prove that every admissible solution is unbounded. Finally, when a = c , we prove that every admissible solution converges to zero.

Convex sets and inequalities.

Takahasi, Sin-Ei, Takahashi, Yasuji, Miyajima, Shizuo, Takagi, Hiroyuki (2005)

Journal of Inequalities and Applications [electronic only]

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On the convergence of the Ishikawa iterates to a common fixed point of two mappings

Ljubomir B. Ćirić, Jeong Sheok Ume, M. S. Khan (2003)

Archivum Mathematicum

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Let C be a convex subset of a complete convex metric space X , and S and T be two selfmappings on C . In this paper it is shown that if the sequence of Ishikawa iterations associated with S and T converges, then its limit point is the common fixed point of S and T . This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].