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Using classical analytic techniques, the Wilker–Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the Sandor–Bencze inequality.

This paper deals with a new generalization of the Garfunkel–Bankoff inequality by introducing a parameter, which relaxes the conditions of the Garfunkel–Bankoff inequality. As applications, an improved version of the Finsler–Hadwiger inequality is obtained.

In this work, we first prove a generalized version of a parameterized Jordan-type inequality. We then use it to prove the generalized versions of Janous’s inequality and Tsintsifas’s inequality which reduce to two inequalities conjectured by Janous and Tsintsifas as special cases.

A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality due to Zhu [S.H. Wu, On generalizations and refinements of Jordan type inequality, Octogon Math. Mag. 12(1) (2004) 267–272] is corrected.

This paper deals with a generalization of L’Hospital-type rules for monotonicity. The result is then used to establish a class of two-sided bounding inequalities for higher-order differentiable functions. As consequences, some refined upper and lower bounds for exponential function, logarithmic function, trigonometric functions and hyperbolic functions are derived.

This paper deals with a new generalized and sharp version of Jordan’s inequality which is a unified generalization of some known results. An application of our results to the improvement of the Yang Le inequality is provided in this paper.

In this work, we extend Jordan’s inequality to obtain a new type of inequality involving functions and their higher-order derivatives. The result is then used to obtain some higher accurate inequalities of Jordan type.

In this work, we present a new sharpened version of the classical Neuberg–Pedoe inequality. As an application, the following improved Neuberg–Pedoe inequality is derived: a 1 2 θ ( b 2 2 θ + c 2 2 θ − a 2 2 θ ) + b 1 2 θ ( c 2 2 θ + a 2 2 θ − b 2 2 θ ) + c 1 2 θ ( a 2 2 θ + b 2 2 θ − c 2 2 θ ) ≥ 3 ( 16 / 3 ) θ F 1 θ F 2 θ + 2 ( a 1 θ b 2 θ − a 2 θ b 1 θ ) 2 + 2 ( a 1 θ b 1 θ ( b 2 θ + c 2 θ − a 2 θ ) ( c 2 θ + a 2 θ − b 2 θ ) − a 2 θ b 2 θ ( b 1 θ + c 1 θ − a 1 θ ) ( c 1 θ + a 1 θ − b 1 θ ) ) 2 .

In this work, a weighted generalization of Rado’s inequality and Popoviciu’s inequality is given, from which some valuable inequalities of Rado–Popoviciu type are derived. Moreover, the result is used to obtain refinements of weighted mean value inequalities.