中文摘要：

Fixed point and common fixed point results for mappings satisfying quasicontractive conditions expressed in the terms of c-distance on TVS-valued cone metric spaces(without the underlying cone which is not normal) are obtained, and P-property and Q-property for mappings in the terms of c-distance are discussed. Our results generalize and improve many known results.

英文摘要：

In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.