Some new Fejér type inequalities via quantum calculus on finite intervals

Abstract

Some new inequalities of Fejér type for twice differentiable mappings are established via quantum calculus on finite intervals. The results presented are extensions of those given earlier. KEYWORDS: integral inequalities, differentiable mappings, Chebyshev quantum integral inequality MSC2010: 26D10 34A08 26D15

On generalizations of some integral inequalities for preinvex functions via $(p,q)$-calculus

“…Furthermore, they investigated the existence and uniqueness results of initial value problems for first and second order impulsive qdifference equations. In recent years, the q-calculus has been studied in various inequalities such as Hermite-Hadamard, Hermite-Hadamard-like, Ostrowski, Fejér, Hanh, and Simpson inequalities, see [19][20][21][22][23][24][25][26][27] and the references cited therein for more details. Especially, Simpson type inequalities have been also studied by using q-calculus for convex and preinvex functions by many researchers, see [28][29][30][31][32][33][34][35][36][37][38][39] and the references cited therein for more details.…”

On the refinements of some important inequalities via $(p,q)$-calculus and their applications

“…Note that if we take p = 1 in Theorem 1.7, then we have the q-Hermite-Hadamard inequality; for more detail, see [20,22,23,25,26]. Besides, we are also directed to some recent work related to other type quantum integral inequalities; see, for instance, [1,3,6,24,28,33,36] and the references therein.…”

Different types of quantum integral inequalities via ( α , m ) $(\alpha ,m)$ -convexity

“…For more details on the inequality ( 1.3 ), see [ 15 , 18 , 20 , 21 , 23 ]. For other type quantum integral inequalities, the interested reader can refer to [ 3 , 4 , 27 , 29 , 31 ].…”