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In this paper, an unity of Mitrinovic–Adamovic and Cusa–Huygens inequalities for circular functions is established, and the analogue one of Lazarevic and Cusa–Huygens-type inequalities for hyperbolic functions is presented. At the same time, the new inequality for circular functions is extended to another interval.
In this paper, sharp Mitrinovic–Adamovic type inequalities for circular functions is established, and the analogue one of Lazarevic-type inequalities for hyperbolic functions is proved by a simple method. At the same time, the new double inequality for circular functions is extended to another interval.
This paper reveals a new relation between the two functions $$ A_{p}\left( x\right) =$$ A p x = $$\left( \int _{0}^{x}e^{-t^{p}}dt\right) /x$$ ∫ 0 x e - t p d t / x and $$B_{q}\left( x\right) =$$ B q x = $$1-\left( 1-e^{-qx^{p}}\right) /\left( q\left( p+1\right) \right) $$ 1 - 1 - e - q x p / q p + 1 . At the same time, we...
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