Based on the work of Agarwal et al., in press, we introduce a concept of generalized eventual cyclic gross contractive mapping in metric spaces, which is a generalization of the eventual cyclic gross contractions. Furthermore, we analyze the existence of a fixed point for this type of contractive mapping, and present a new and general fixed point theorem.
We are concerned with the existence of mild solutions to the Cauchy problem for fractional evolution equations of neutral type with almost sectorial operatorswhere 0
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