Abstract:
As the title suggests, the present dissertation deals with the refinements of Jensen-
Steffensen and related inequalities. We extend some classical results and give some
new refinements of several well known inequalities including Jensen’s inequality, Jensen-
Steffensen inequality, Hermite-Hadamard inequality, majorization-type inequality,
generalized weighted Favard and Berwald inequalities. We also provide the refine-
ments of some companion inequalities to the Jensen’s inequality, namely Slater’s
inequality and the inequalities obtained by M. Mati ́ and J. Peˇari ́ in [44]. We
c
c c
sharpen the lower bounds of the Jensen’s functional. Some inequalities in terms of
Gˆteaux derivatives for convex functions are also provided. Finally, we present not
aonly the generalizations of Hardy-Littlewood-P ́lya inequality [26, Theorem 134] but
o also generalizations of some results given in [8] and [36].
