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A mixed monotone variational inequality (MMVI) problem in a Hilbert space is formulated to find a point such that for all , where is a monotone operator and is a proper, convex, and lower semicontinuous function on . Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the work of Wang et al., (2001) has in general weak convergence in an infinite-dimensional space, and the algorithm introduced in the paper of Noor (2001) fails in general to converge to a solution.

Over the past century and a half, global technological leadership has shifted from Europe to the United States, while scholars argue that the world has seen that it is now shifting from the United States to China due to China's extraordinary catch-up in the past four decades, in which the public policy-oriented national innovation system development plays a critical role that might provide an alternative way for innovation-driven development especially for emerging markets. Even though encountering many challenges ahead, China is positioning itself to take over the global innovation leadership in the next few decades. Here in this article, we introduce a serious yet underexplored question: could China go beyond catch-up and become the global innovation powerhouse? Specifically, drawing from the holistic innovation perspective, which is an original theoretical paradigm for the mission-oriented innovation policy change, this article critically reviews, both qualitatively and quantitatively, China's remarkable innovation progress and main drivers in comparison with G7 countries plus South Korea and India, trying to provide a comprehensive and critical view of state-of-the-art research on China's innovation catch-up. We further explore the five major challenges that China must take seriously when marching toward the global innovation powerhouse. Finally, we propose a mission-oriented holistic STI policy design framework for both China and other emerging economies to go beyond catch-up in a competitive dynamic world. This article provides a new and holistic perspective to access China's innovation progress and challenges, also generates novel insights for scholars and public agencies to contribute to global innovation development, with a shared goal of achieving global sustainable development in the post-COVID-19 pandemic world. [ABSTRACT FROM AUTHOR]

Innovation is the driver and accelerator for high-quality economic development and the transformation and upgrading of enterprises. At present, the world is undergoing significant changes unseen over the last century. Faced with the new world economic pattern and the new international relations in the postpandemic era, China should systematically clarify the prominent problems with the current scientific and technological (S&T) system, and establish new technological innovation strategies in the new era and new economic landscape, which are of great significance. Especially in the context of the new pattern of development, it is greatly highlighted how to systematically lower over-dependence on core technologies and resolve bottleneck problems with core technology arising from excessive attention to the international economic flows. Based on the medium- and long-term strategic background of the current new pattern of development, this paper explores the prominent problems of the S&T innovation system under the background of the new pattern of development from the perspectives of innovation policy system, regional innovation system, and enterprise innovation mode. Meanwhile, the paper believes that the innovation guidance system under the new pattern of development needs to be realized based on the guidance of the new innovation strategy of "opening thinking based on bottom lines and comprehensive indigenous innovation," and also the three leading paths of holistic innovation guided by the new pattern of the whole national institutional system, the future industry, and the world-class enterprises. Only in this way can China become a power in terms of S&T innovation in the world. [ABSTRACT FROM AUTHOR]

The article focuses on the evolution of entrepreneurship in the context of China's economic and social development, emphasizing the importance of benefit corporation entrepreneurship in the new era. The topics include the role of entrepreneurship in China's economic transformation, the evolution of entrepreneurship through different stages, and the policy importance of cultivating benefit corporation entrepreneurship for high-quality economic and social development.

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