Abstract:
The
vii
study
presents
some
of
the
fundamental
results
annexed
to
the
Hermite Hadamard inequality. It aims at improving the role of distinct classes of convexity
in the theory of Inequalities. This dissertation is devoted to sift out several refinements,
generalizations, improvements and extensions of the Hermite Hadamard type inequalities
for functions whose absolute values of first and second derivatives belong to class of
convex functions. Eventually, as applications, the obtained results are employed for
special means of real numbers. Explicit bounds are also being derived to versatile composite
quadrature rules in terms of variety of functions belonging to different classes of convex
functions.
The analysis sets aside the determination of the partition required that would ensure
that the accuracy of the result would be within a prescribed error tolerance. This way, this
thesis caters a study of some inequalities analogous to the most acclaimed and basic
Hadamard inequality. The study piles up interesting developments in this research field
under a unified framework. This work will be of keenness to mathematical analysts, pure
and applied mathematicians, physicists, engineers, computer scientists and other areas of
science.