Generation of new fractional inequalities via n polynomials s-type convexity with applications

Abstract

The celebrated Hermite–Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite–Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing $\mathcal{K}$ K -fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning.

Estimates of quantum bounds pertaining to new q-integral identity with applications

“…A bivariate real-valued function Υ : (0, ∞) × (0, ∞) → (0, ∞) is said to be a bivariate mean if min{ε, ζ } ≤ Υ (ε, ζ ) ≤ max{ε, ζ } for all ε, ζ ∈ (0, ∞). It is well known that the bivariate means are closely related to many special functions [8,19,26,30,31,44,45]. Recently, the inequalities between different bivariate means have attracted the attention of many researchers [27-29, 43, 47, 50].…”

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

“…The inequality (1.1) has gained considerable attention, as convex analysis and fractional calculus operators involving several classes of convex functions is an uphill task. Therefore many authors proposed different numerical techniques to find Simpson-type inequalities, arising in the substantial literature of numerical analysis and engineering, and many other fields of sci-ences [1][2][3][4][5][6][7][8][9][10][11][12]. Profusely novel versions of Simpson-type inequalities for the class of convex functions have been modified and generalized by numerous researchers [13][14][15][16][17][18][19][20][21][22][23][24].…”

On New Modifications Governed by Quantum Hahn’s Integral Operator Pertaining to Fractional Calculus

“…Inequality plays an irreplaceable role in the development of mathematics. Very recently, many new inequalities such as Hermite-Hadamard type inequality [34][35][36][37][38], Petrović type inequality [39], Pólya-Szegö type inequality [40], Ostrowski type inequality [41], reverse Minkowski inequality [42], Jensen type inequality [43,44], Bessel function inequality [45], trigonometric and hyperbolic function inequalities [46], fractional integral inequality [47][48][49][50][51], complete and generalized elliptic integral inequalities [52][53][54][55][56][57], generalized convex function inequality [58][59][60], and mean value inequality [61][62][63] have been discovered by many researchers. In particular, the applications of integral inequalities have gained considerable importance among researchers for fixed-point theorems; the existence and uniqueness of solutions for differential equations [64][65][66][67][68] and numerous numerical and analytical methods have been recommended for the advancement of integral inequalities [69][70][71][72][73][74]…”