Ostrowski type integral inequalities for functions of bounded variation and applications

This thesis work consists of two main parts. In the first part, some generalized Ostrowski type inequalities are first proved for the function of bounded variation with one variable and special cases of these inequalities are analyzed. Moreover, some generalized inequalities are established for the mappings whose derivatives and th derivatives are of bounded variation, respectively. Then, some significant weighted inequalities are proved for the functions of bounded variation and the functions whose derivatives are of bounded variation. Moreover, some quadrature formula for numerical integration are given and some bounds for the remainder term are established with the help of obtained inqualities. In the second main part, some Ostrowski type inequalities are obtained for the functions of bounded variation with two variable. Weighted versions of these inequalities are also proved.