Abstract:
The aim of this paper is to introduce a new type of two-dimensional convexity by using totalorder
relations. In the first part of this paper, we examine the Hyers–Ulam stability of two-dimensional
convex mappings by using the sandwich theorem. Our next step involves the development of
Hermite–Hadamard inequality, including its weighted and product forms, by using a novel type of
fractional operator having non-singular kernels. Moreover, we develop several nontrivial examples
and remarks to demonstrate the validity of our main results. Finally, we examine approximate convex
mappings and have left an open problem regarding the best optimal constants for two-dimensional
approximate convexity.
