On Generalized Strongly p-Convex Functions of Higher Order

Abstract

The aim of this paper is to introduce the definition of a generalized strongly p-convex function for higher order. We will develop some basic results related to generalized strongly p-convex function of higher order. Moreover, we will develop Hermite–Hadamard-, Fejér-, and Schur-type inequalities for this generalization.

Midpoint Inequalities via Strong Convexity Using Positive Weighted Symmetry Kernels

“…for all β 1 , β 2 ∈ I and l ∈ ½0, 1. See [5,28,29] and references therein for more detail about strongly convex functionality.…”

“…The new fractional integral inequalities in convexity are always appreciable. Moreover, the generalized and new mode of convexity is the area of interest for most of researcher of convex analysis [5,6].…”

A Note on Generalized Strongly p-Convex Functions of Higher Order

“…Several researchers have been considered for classical convexity such that some of these new concepts are based on an extension of the domain of convex functions or sets to a generalized form [3][4][5][6][7][8][9]. Some examples of these new concepts are quasiconvexity [10], exponential convexity [11,12], logarithmical convexity [13], ℎ-convexity [14,15], and 𝑝-convexity [3,4,16,17]. 𝑝-Convex funtions and their properties was introduced by Zhang and Wan [16] in 2007.…”

“…In 2018 Maden et al [17] discussed strongly 𝑝-convex funtions and Hermite-Hadamard inequality for it. In 2020, Saleem et al [3,4] discussed about generalized 𝑝-convex funtions and generalized strongly 𝑝-convex funtions of higher order.…”

“…In [3] discussed definition and properties of generalized strongly 𝑝-convex functions of higher order also some of type inequalities which are Hermite-Hadamard, Fejér, and Schur. In Schur type inequality for generalized strongly 𝑝-convex funtions of higher order in [3] 𝑝 with 𝑞 > 0 and 𝜙(𝑡) = 𝑡 𝑞 (1 − 𝑡) + 𝑡(1 − 𝑡) 𝑞 . So, this paper revises the correction of Schur type inequality in [3].…”