Abstract. In this article, we prove that the double inequalityholds true for all a, b > 0 with a = b if and only if α ≥ 5/9 and β ≤ 1 − 1/[2 log(1 + √2)] = 0.4327 · · · , where G(a, b), C(a, b) and M (a, b) are respectively the geometric, contraharmonic and Neuman-Sndor means of a and b.

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Objective. To explore the change in the medical serviceability of primary hospitals since the establishment of the Huzhou No. 1 People’s Hospital medical care group incorporating the integrated delivery system. Methods. With reference to the “Grade Evaluation Standard of General Hospitals in Zhejiang Province” and the “Guidelines for Service Capacity Evaluation of Township Hospitals (2019 Edition),” we analyzed the influence of the integrated delivery system on the capacity of primary medical services and selected the targeted core indicators. From the four dimensions of diagnosis and treatment breadth, diagnosis and treatment efficiency, surgical ability, and patient satisfaction, an index evaluation system was established to explore the changes in the medical serviceability in primary hospitals. Results. The measurements were aimed at four specific issues, that is, the low medical technology level of grassroots personnel, the poor information communication among medical institutions, the difficulty in recruiting people, and the imperfect training mechanism in primary hospitals. After establishing a series of measurements related to the problems faced by the primary healthcare sector in China, the score of breadth of diagnosis and treatment, efficiency of diagnosis and treatment ability, surgical ability, and patient satisfaction of the primary hospitals in our medical group have greatly increased. Conclusion. The integrated delivery system improved the primary hospitals’ medical health ability obviously. Our study also provides various useful and operable suggestions for primary healthcare.

In this paper, we find the least value α and the greatest value β such that the double inequalityholds true for all a, b > 0 with a = b, where P(a, b), M(a, b) and Q(a, b) are the first Seiffert, Neuman-Sándor and quadratic means of a and b, respectively. MSC: 26E60

For any α∈0,1, we answer the questions: what are the greatest values p and λ and the least values q and μ, such that the inequalities Lpa,b<Iαa,bL1-αa,b<Lqa,b and Lλa,b<αIa,b+1-αLa,b<Lμa,b hold for all a,b>0 with a≠b? Here, Ia,b, La,b, and Lpa,b denote the identric, logarithmic, and pth Lehmer means of two positive numbers a and b, respectively.