Non-newtonian calculus and general convexity

ABSTRACT Master Thesis NON-NEWTONIAN CALCULUS AND GENERAL CONVEXITY Muhammet ÖZBUCAK Ağrı İbrahim Çeçen University Graduate School of Natural and Applied Sciences Department of Mathematics Supervisor: Dr. Öğr. Üyesi Alper EKİNCİ The purpose of the present thesis is to give information related with non-newtonien arithmetic and to show the relation with convexity of it. It was introduced the alpha arithmetic and was given some applications of well-know arithmetic. Moreover, it was given some informations conceming convexity, inequalities, clasical inequalities, and non-newtonien calculus. Finally, it was given place to the definition of convexity in the non-newtonien calculus. 2019, 61 pages Keywords:Hermite-Hadamardtypeinequalities, Hölder inequality, Power-mean inequality, convex functions, conformable fractional integrals.