In this paper we consider some classes of α-preinvex and α-invex functions. We study some properties of these classes of α-preinvex (α-invex) functions. In particular, we establish the equivalence among the α-preinvex functions, α-invex functions and αη-monotonicity of their differential under some suitable conditions.

In this paper, we derive several weighted Hermite-HadmardNoor type inequalities for the differentiable preinvex functions and quasi preinvex functions. AMS (MOS) Subject Classification Codes: 26D15, 26D20, 26D07

In this paper, we present weighted integral inequalities of Hermite-Hadamard type for differentiable preinvex and prequasiinvex functions. Our results, on the one hand, give a weighted generalization of recent results for preinvex functions and, on the other hand, extend several results connected with the Hermite-Hadamard type integral inequalities. Applications of the obtained results are prov...

In this paper, we define and introduce some new concepts of strongly φ-preinvex (φ-invex) functions and strongly φη-monotone operators. We establish some new relationships among various concepts of φ-preinvex (φ-invex) functions. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previous...

In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

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...