On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals

Abstract

In this paper, we introduce the generalized k-fractional integral in terms of a new parameter k > 0, present some new important inequalities of Pólya-Szegö anď Cebyšev types by use of the generalized k-fractional integral. Our consequences with this new integral operator have the abilities to implement the evaluation of many mathematical problems related to real world applications.

New generalized Pólya–Szegö and Čebyšev type inequalities with general kernel and measure

“…Recently, Saima et al in [49] generalized the definition of operator given in Definition 1.4 stated as follows. Definition 1.7 Let (a, b) be a finite or infinite interval on the real line together with k > 0.…”

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]…”

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

“…For some recent trends in quantum calculus, the interested readers are referred to [12-14, 16, 17, 35]. Recently, Tariboon and Ntouyas [36] introduced the notions of quantum derivative and quantum integral on finite intervals and developed various q-analogues of classical integral inequalities, such as Hölder inequality [49], Hermite-Hadamard inequality [3,7,9,15,20,21,33], Petrović inequality [1], Pólya-Szegö and Čebyšev inequalities [32], Jensen inequality [2,5,18].…”