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The nucleating effect of silk fibroin nano-disc (SFN) on the crystallization behavior of poly(L-lactic acid) (PLLA) was investigated by simultaneous synchrotron small-and wide-angle X-ray scattering measurements. For the isothermal crystallization at 110 °C from the melt, the induction period of the PLLA specimens containing 1% SFN was reduced compared to that of the neat specimens, indicating the acceleration of the nucleation of PLLA. The final degree of crystallinity was also increased, and the crystallization half-time was decreased, which indicates that the overall crystallization process was accelerated. Furthermore, the final value of the crystallite size (the lateral size of the crystalline lamella) was slightly lower for the specimens

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The goal of this paper is to define rational contraction in the context of A-metric spaces and to develop various fixed-point theorems in order to elaborate, generalize, and synthesize several previously published results. Finally, to illustrate the new theorem, an example is given.