In this paper, we establish some new Hermite-Hadamard type integral inequalities involving two log-preinvex functions. Note that log-preinvex functions are nonconvex functions and include the log-convex functions as special cases. As special cases, we obtain the well known results for the convex functions.

The present paper deals with the properties of geodesic η-preinvex functions and their relationships with η-invex functions and strictly geodesic η-preinvex functions. The geodesic η-pre-pseudo-invex and geodesic η-pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.

The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h)-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some...

Abstract In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex functions by using Riemann–Liouville fracti...

A class of functions called E-B-vex functions is defined as a generalization of E-convex and B-vex functions. Similarly, a class of E-B-preinvex functions, which are generalizations of E-convex and B-preinvex functions, is introduced. In addition, the concept of B-linear functions is also generalized to E-B-linear functions. Some properties of these proposed classes are studied. Furthermore, th...

Abstract In this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions Wolfe type as well Mond–Weir duality theorems under semilocal E -preinvex functions. Furthermore, present saddle-point criteria to relate optimal solution programming a saddle point Lagrangian function.

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

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...