Integral Inequalities Involving Strongly Convex Functions

Abstract

We study the notions of strongly convex function as well as -strongly convex function. We present here some new integral inequalities of Jensen's type for these classes of functions. A refinement of companion inequality to Jensen's inequality established by Matić and Pečarić is shown to be recaptured as a particular instance. Counterpart of the integral Jensen inequality for strongly convex functions is also presented. Furthermore, we present integral Jensen-Steffensen and Slater's inequality for strongly convex functions.

Association of Jensen’s inequality for s-convex function with Csiszár divergence

“…Convex function has wide applications in pure and applied mathematics, physics, and other natural sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]; it has many important and interesting properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] such as monotonicity, continuity, and differentiability. Recently, many generalizations and extensions have been made for the convexity, for example, s-convexity [38], strong convexity [39][40][41], preinvexity [42], GA-convexity [43], GG-convexity [44], Schur convexity [45][46][47][48]…”

Inequalities Involving Conformable Approach for Exponentially Convex Functions and Their Applications

“…A bivariate function Ω: (0, ∞) × (0, ∞) ⟶ (0, ∞) is said to be a mean if min a, b { } ≤ Ω(a, b) ≤ max a, b { } for all a, b ∈ (0, ∞). Recently, the bivariate means have been the subject of intensive research [63][64][65][66][67][68][69][70][71][72][73][74][75]; in particular, many remarkable inequalities and properties for the bivariate means and their related special functions can be found in the literature [76][77][78][79][80][81][82][83][84][85].…”

Some New Hermite–Hadamard-Type Inequalities Associated with Conformable Fractional Integrals and Their Applications

“…In particular, many remarkable inequalities and properties for the convex functions can be found in the literature . Recently, a great deal of generalizations, extensions, and variants have been made for the convexity [65][66][67][68][69][70][71][72].…”