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Abstract: Let be a given real number, and , be two parameters, and let We determine the values which provide the best approximation: Furthermore, we establish a sharp Jordan’s inequality, and then apply it to improve the Yang Le inequality. [Copyright &y& Elsevier]

This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009-2012 are included to stimulate new interest in future study and research. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This paper deals with a generalization of L’Hôspital-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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: A new generalized version of Aczél’s inequality is proved. This is a unified generalization of some known results. Moreover, the result is applied to the improvement of the well-known Bellman’s inequality. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This paper deals with existence theorems of positive solutions for singular elliptic boundary value problems in a ball. The results of this paper are generalizations of those proved by authors cited in the references. [Copyright &y& Elsevier]