Sequences which satisfy a logarithmic linear inequality

• Autorzy: Stević S.
• Języki publikacji: EN

Abstrakty

EN

In this note we discuss the boundedness and convergence of a sequence which satisfies the following logarithmic linear inequality where k(1) + k(2) +... + km = 1. We focus our attention especially to the case n = 2. Also we describe a situation where this inequality occurs naturally.

Słowa kluczowe

EN

sequence; logarithmic linear inequality; boundedness

PL

ciąg matematyczny; nierówność logarytmiczna liniowa; ograniczoność

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2004
• Tom: Nr 34
• Strony: 85--95
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Stević S.

• Matematički Fakultet, Studentski Trg 16, 11000 Beograd, Serba, Yugoslavia

Bibliografia

• [1] J. Bibby, Axiomatisations of the average and a further generalisation of monotonic sequences, Glasgow Math. J. 15(1974), 63-65.
• [2] D. Borwein, Convergence criteria for bounded sequences, Proc. Edinburgh Math. Soc. 18(2)(1972), 99-103.
• [3] E. Camouzis, E.A. Grove, G. Ladas, V.L. Kocic, Monotone unstable solutions of difference equations and conditions for boundedness, J. Differ. Equations Appl. 1(2)(1995), 17-44.
• [4] E.T. Copson, On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. 17(2)(1970), 159-164.
• [5] J.D. Kečkić, A remark on a generalization of monotonic sequences, Publ. Inst. Math. (Beograd) 16(30)(1973), 85-89.
• [6] V. lstratescu, On some classes of operators I, Math. Balkan. 2(1972), 49-57.
• [7] D.C. Russell, On bounded sequences satisfying a linear inequality, Proc. Edinburgh Math. Soc. 19(1973), 11-16.
• [8] S. Stević, A note on bounded sequences satisfying linear inequality, Indian J. Math. 43(2)(2001), 223-230.
• [9] S. Stević, A generalization of the Copson's theorem concerning sequences which satisfy a linear inequality, Indian J. Math. 43(3)(2001), 277-282.
• [10] S. Stević, On the recursive sequence x_n+1 = - (1 / x_n) + (A / x_n-1), lnt. J. Math. Sci. 27(1)(2001), 1-6.
• [11] S. Stević, A global convergence results with applications to periodic solutions, Indian J. Pure Appl. Math. 33(1)(2002), 45-53.
• [12] S. Stević, Asymptotic behaviour of a sequence defined by iteration with applications, Colloq. Math. 93(2)(2002), 267-276.
• [13] S. Stević, A global convergence result, Indian J. Math. (to appear).