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Necessary and sufficient conditions for oscillations of delay partial difference equations

Bing Gen Zhang, Shu Tang Liu (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is concerned with the delay partial difference equation (1) A m + 1 , n + A m , n + 1 - A m , n + Σ i = 1 u p i A m - k i , n - l i = 0 where p i are real numbers, k i and l i are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.

Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation

Ethiraju Thandapani, L. Ramuppillai (1999)

Kybernetika

In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form Δ 2 y n - 1 + q n y σ ( n ) γ = g n , where γ is a quotient of odd positive integers, in the superlinear case ( γ > 1 ) and in the sublinear case ( γ < 1 ) .

Nonlinear stability of a quadratic functional equation with complex involution

Reza Saadati, Ghadir Sadeghi (2011)

Archivum Mathematicum

Let X , Y be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping f : X Y satisfies f ( x + i y ) + f ( x - i y ) = 2 f ( x ) - 2 f ( y ) for all x , y X , then the mapping f : X Y satisfies f ( x + y ) + f ( x - y ) = 2 f ( x ) + 2 f ( y ) for all x , y X . Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.

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