On φ-convex functions

Abstract

Abstract. In this paper we introduce the notion of ϕ -convex functions as generalization of convex functions. Some basic results under various conditions for the function ϕ are investigated. Moreover, we establish Jensen and Hermite-Hadamard type inequalities related to ϕ -convex functions. Also, the notions of ϕ b -convex and ϕ E -convex functions, which are generalization of ϕ -convex functions are introduced and some new results related to these new settings are obtained.Mathematics subject classification (2010): 26A51, 26D15, 52A01.

Some Hermite-Hadamard-Fejér Type Integral Inequalities for Differentiable η-Convex Functions with Applications

“…On the other hand, the concept of -convex functions, firstly named by -convex functions, as generalization of convex functions has been introduced in [9].…”

Inequalities via generalized log ⁡m-convex functions

“…An important extension of convex functions is an intermediate form between the usual convexity and star shaped property is m-convex function, defined by the Toader [24]. Gordji et al [10] also introduced an important class of convex functions, which is called ϕ-convex function. These ϕ-convex functions are nonconvex functions.…”

“…These ϕ-convex functions are nonconvex functions. For recent developments, see [6,7,10,19,20] and the references therein.…”

halida Inayat Noor, Farhat Safdar, Integral inequalities via generalized (a, m)-convex functions

“…Gordji et al [11] introduced a new class of convex functions involving the bifunction, which is called φ -convex functions. These φ -convex functions are not convex functions.…”

“…These φ -convex functions are not convex functions. For the recent developments, see [11,12,13,14] and the references therein.…”