Generalizations of Hölders inequality

Some generalized Hölder's inequalities for positive as well as negative exponents are obtained.published_or_final_versio

Some discrete Poincaré-type inequalities

Some discrete analogue of Poincaré-type integral inequalities involving many functions of many independent variables are established. These in turn can serve as generators of further interesting discrete inequalities.published_or_final_versio

Some new nonlinear retarded sum-difference inequalities with applications

The main objective of this paper is to establish some new retarded nonlinear sum-difference inequalities with two independent variables, which provide explicit bounds on unknown functions. These inequalities given here can be used as handy tools in the study of boundary value problems in partial difference equations. © 2011 Wang et al; licensee Springer.published_or_final_versio

Two Ostrowski type inequalities for the stieltjes integral of monotonic functions

Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonie integrators and Holder continuous integrands while the second considers the dual case, that is, for monotonie integrands and Holder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented. Copyright Clearance Centre, Inc.postprin

Sharp Cusa and Becker-Stark inequalities

We determine the best possible constants θ,ϑ,α and β such that the inequalities ((2+cosx)/3)^θ < sinx/x < ((2+cosx)/3)^ϑ and ((π^2)/(π^2-4×^2))^α < tan×/× < ((π^2)/(π^2-4×^2))^β are valid for 0 < × < π/2. Our results sharpen inequalities presented by Cusa, Becker and Stark.published_or_final_versio

Reverse Beckenbach-Dresher’s Inequality

published_or_final_versio

On the Quermassintegrals of Convex Bodies

published_or_final_versio

On improvements of Opial-type inequalities

In the present paper, we establish some new Opial-type integral inequalities in two variables. The results in special cases yield some of the interrelated results on Godunova–Levin's and Mitrinović–Pečarić's inequalities. These results provide new estimates on inequalities of this type.published_or_final_versio

Design and evaluation of two blended learning approaches: Lessons learned

In this paper, we share two blended learning approaches used at the National Institute of Education in Singapore. We have been using these two approaches in the last twelve years in many courses ranging from the diploma to graduate programs. For the first blended learning approach, we integrated one asynchronous communication tool with face to face tutorials, classroom discussions, and a reflection session. For the second blended learning approach, we integrated two asynchronous tools with face to face tutorials in a course. We discuss the theoretical foundation of the two blended learning approaches. In addition, we share insights from these two blended learning approaches, based on the students' data (online postings, questionnaires, reflection logs, and interviews), as well as our own reflections. Finally, we describe and discuss several important lessons learned that could inform the design of future instructional strategies in implementing blended learning in university teaching and learning settings.published_or_final_versio

An Opial-Type Inequality in Time Scales

published_or_final_versio