Search

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]

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: 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]