New integral inequalities for local fractional integrals and applications

As it is known in mathematics, fractal curves are everywhere continuous but nowhere differentiable. Therefore, classical analysis is inadequate to handle and characterize such curves. Local fractional analysis has become a tool for describing the events on fractals and the behavior of functions that are everywhere continuous but nowhere differentiable. From this point of view, the aim of the thesis is to contribute to the field of local fractional analysis and to solve the deficiencies in the field by obtaining the inequalities which are not existed in the literature related to the theory of local fractional analysis . For this purpose, the thesis consists of four sections. In the first section, the historical process of inequality and local fractional analysis theories is mentioned. In the second section, information is given about the Cantor fractal set studied. In addition, information about the Ra space which is established by Yang and providing a new analysis has been given and the basic theorems and properties for local fractional limit, continuity, derivative, integral defined by using this information have been given. In the third section, by using local fractional integration new inequalities such as Steffensen, Cˇ ebyšev, Grüss are obtained. In the last section, conclusions and recommendations related to this subject are given.