Mean value in invexity analysis

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Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m) -preinvex functions (2016, background): “For more details please see [1, 33] and the references therein.”
Invex sets and preinvex functions on Riemannian manifolds (2007, background): “In Section 6 we extend the mean value theorem for differentiable functions defined on invex sets in R to differentiable functions on invex subsets of Riemannian manifolds (see [1,2]).”
On hermite-hadamard inequalities for h-preinvex functions (2014, background): “For the applications, properties and other aspects of the preinvex functions, see [1, 3, 11, 15, 16, 24, 33].”
Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex (2012, methodology): “Now, we recall some notions in invexity analysis which will be used throughout the paper (see [14, 16] and references therein).”
On Hadamard integral inequalities involving two log-preinvex functions. (2007, background): “From Definition 2.5, we have log f (u + tη(v, u)) ≤ (1 − t) log(f (u)) + t log(f (v)), ∀u, v ∈ K, t ∈ [0] [1].”
Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems (2009, methodology): “We shall use the following mean-value theorem for invex functions to prove one of the main results of this paper. Theorem 2.1 See [ 18 ] and [22].”