Qi type integral inequalities

Integral inequalities have been frequently employed in the theory of functional analysis, differential equations and applied sciences such as probability and statistics. Recently, especially an integral inequaliy, which is called Qi Inequality by mathematics community, has been studied by many authors. In this thesis, we are concerned with Qi type integral inequalities. We present many conjectures on these kind of inequalities. Then, we investigate many papers which gives affirmative answer on these conjectures. The organization of this thesis is as follows: In Chapter 1, we give the necessary inequalities and some definitions. In Chapter 2, we present Qi's open problem and related problems as conjectures. In Chapter 3, we consider five papers on Qi type integral inequalities from 2001 through 2003. In Chapter 4, we present four papers on Qi type integral inequalities from 2004 through 2005. In Chapter 5, we look at five papers on Qi type integral inequalities in 2006. In Chapter 6, we present four papers on Qi type integral inequalities from 2007 through 2009.