in this paper,  we introduce  the notion of $m$-fuzzifying interval spaces, and discuss the relationship between $m$-fuzzifying interval spaces and $m$-fuzzifying convex structures.it is proved that  the category  {bf mycsa2}  can be embedded in  the category  {bf  myis}  as a reflective subcategory, where  {bf mycsa2} and   {bf  myis} denote  the category of $m$-fuzzifying convex structures of...

In the frame of fractional calculus, term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus objective this review paper present Hermite–Hadamard (H-H)-type inequalities involving a variety classes convexities pertaining integral operators. Included various are classical convex functions, m-convex r-convex (α,m)-convex (α,m)-geometric...

The minimum of quadratic functionals of the gradient on the set of convex functions ABSTRACT We study the innmum of functionals of the form R Mruru among all convex functions u 2 H 1 0 (() such that R jruj 2 = 1. (is a convex open subset of R N , and M is a given symmetric N N matrix.) We prove that this innmum is the smallest eigenvalue of M if is C 1. Otherwise the picture is more complicated...

This paper discusses computational complexity of conceptual successive convex relaxation methods proposed by Kojima and Tunn cel for approximating a convex relaxation of a compact subset F = fx 2 C 0 : p(x) 0 (8p() 2 P F)g of the n-dimensional Euclidean space R n. Here C 0 denotes a nonempty compact convex subset of R n , and P F a set of nitely or innnitely many quadratic functions. We evaluat...

We find a different approach to define convex functions in the subRiemannian setting. A function on a sub-Riemannian manifold is nonholonomically geodesic convex if its restriction to any nonholonomic (straightest) geodesic is convex. In the case of Carnot groups, this definition coincides with that by Danniell-Garofalo-Nieuhn (equivalent to that by Lu-Manfredi-Stroffolini). Nonholonomic geodes...

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...