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Keywords:
fixed point; sum of operators; non-autonomous difference equations; positive solution
fixed point; sum of operators; non-autonomous difference equations; positive solution
Summary:
In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ a $k$-set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.
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