Generalization of some integral inequalities via interval-valued functions

In this thesis, LR-convex interval-valued functions are examined, and new inequalities based on conformable fractional integral operators are obtained for these functions. The thesis consists of four chapters. In the first chapter, the historical developments of inequalities, convex sets and functions, definitions of fractional integrals, interval analysis, and LR-convex interval-valued functions are discussed. The second chapter presents the fundamental definitions and theorems to be used throughout the thesis, providing essential background information for both real-valued and interval-valued functions. In the third chapter, new inequalities are obtained for LR-convex interval-valued functions using conformable fractional integral operators, and new results are reached through appropriate selections. Additionally, it is observed that some studies in the literature have been generalized through special choices of parameters. Finally, the fourth chapter summarizes the results are obtained throughout the thesis and offers suggestions for future research.