Although traditional CPU scheduling efficiently utilizes multiple cores with equal computing capacity, the advent of multicores with diverse capabilities pose challenges to CPU scheduling. For such asymmetric multi-core systems, scheduling is essential to exploit the efficiency of core asymmetry, by matching each application with the best core type. However, in addition to the efficiency, an important aspect of CPU scheduling is fairness in CPU provisioning. Such uneven core capability is inherently unfair to threads and causes performance variance, as applications running on fast cores receive higher capability than applications on slow cores. Depending on co-running applications and scheduling decisions, the performance of an application may vary significantly. This study investigates the fairness problem in asymmetric multi-cores, and explores the design space of OS schedulers supporting multiple fairness constraints. In this paper, we consider two fairness-oriented constraints, minimum fairness for the minimum guaranteed performance and uiformity for performance variation reduction. This study proposes four scheduling policies which guarantee a minimum performance bound while improving the overall throughput and reducing performance variation too. The proposed fairness-oriented schedulers are implemented for the Linux kernel with an online application monitoring technique. Using an emulated asymmetric multi-core with frequency scaling and a real asymmetric multi-core with the big.LITTLE architecture, the paper shows that the proposed schedulers can effectively support the specified fairness while improving overall system throughput.