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This paper investigates convergence behavior of composition sequencesf1∘f2∘…∘fn(z) and fn∘fn−1∘…∘f1(z) where the fn's are bilinear transformations and fn→z.Additional results are provided for the case when the fn's are more general functions

international journal of mathematics and mathematical sciences

Convergence of composition sequences of bilinear and other transformations<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\left\{ {f_n } \right\},f_n \to z$" id="E1"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:math>

Convergence of composition sequences of bilinear and other transformations{fn},fn→z