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In 2009 Qingnian Zhang and Yisheng Song proved fixed point theory for two φ–weak contraction functions. We generalize this result by finding fixed point and coincidence point for three single-valued φ–weak contraction T1, T2, T3 defined on a complete metric space.

In this paper we study conditions that an infinite matrix has to satisfy in order to define a linear bounded operator from any weighted with a weight sequence s={ si} of positive numbers into itself, and give upper and lower estimations of the approximation numbers of such an infinite matrix.