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Abstract: 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 Sándor–Bencze inequality. [Copyright &y& Elsevier]

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]

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: In this paper, we are concerned with the third order two-point generalized right focal boundary value problem A few new results are given for the existence of at least one, two, three and infinitely many monotone positive solutions of the above boundary value problem by using the Krasnosel’skii fixed-point theorem in cones, and the Leggett–Williams fixed-point theorem. [Copyright &y& Elsevier]

Using the theory of majorization, new inequalities for convex sequences are proved. A necessary and sufficient condition for a convex sequence is established. This reveals an important relationship between the convex sequence and the majorized inequality. Finally, some applications of our new inequalities and some improvements of certain known results are presented. [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]

This paper deals with the generalization and sharp versions of the Wolstenholme cyclic inequality and their applications. The inequalities of this paper improve and unify corresponding known results. Several interesting inequalities including the celebrated Ozeki inequality are obtained. Extensions of the Wolstenholme inequality for a complex polygon and the Wolstenholme inequality for a convex quadrilateral are derived. As example of applications, the well-known Erdös–Mordell inequality is improved in this paper. In addition, several extensions, unifications and refinements of Gueron–Shafrir’s inequalities and Mitrinović–Pecaric’s inequality are established. [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: Values of are determined for which there exist positive solutions of the fourth-order singular boundary value problems where , is parameter. For , we give criteria for the existence of eigenfunctions. [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]

Abstract: On the basis of a special cone and the application of the fixed point theory, some new results for the existence of positive solutions of singular Sturm–Liouville boundary value problems on the half-line are obtained. [Copyright &y& Elsevier]

Abstract: The stability of a horizontal layer of fluid heated from below as well as from above is examined. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent part, which is oscillatory. The amplitude of temperature modulation is δ. By considering the weakly non-linear analysis, it is shown that the modulation produces a range of stable hexagons near the critical Rayleigh number. Some comparisons have been made with the other theoretical results. [Copyright &y& Elsevier]

Abstract: Under certain assumptions on the nonlinear–nonhomogenous term of ordinary differential equations associated with fourth order singular boundary value problems, we establish a necessary and sufficient condition for the existence of positive solutions of the boundary value problem by means of fixed point theorems. [Copyright &y& Elsevier]

Abstract: The linear stability of a thin vertical fluid layer heated from below is considered. Here the gravitational field consists of two parts: a constant part and a time-dependent part varying periodically. The time-dependent part has been expressed in Fourier series. The effect of gravity modulation on the fluid layer is examined. Using an asymptotic analysis the convective threshold has been determined. Some comparisons are made with the known results. [Copyright &y& Elsevier]