Simpson’s type integral inequalities for &lt;em&gt;ĸ&lt;/em&gt;-fractional integrals and their applications

Rashid, Saima; Akdemir, Ahmet Ocak; Jarad, Fahd; Noor, Muhammad Aslam; Noor, Khalida İnayat

doi:10.3934/math.2019.4.1087

Cited by 35 publications

(21 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For current research on preinvex functions, concerned readers are referred to [11,48,[53][54][55][56][57][58]. The notion of strongly convex functions was introduced by Karamardian [59] and Polyak [21].…”

Section: Definition 1 ([52])mentioning

confidence: 99%

Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

et al. 2019

Self Cite

View full text Add to dashboard Cite

The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly h -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters h and σ . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.

show abstract

Section: Definition 1 ([52])mentioning

confidence: 99%

Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Humaira et al [45] developed the theory of quantum integral inequalities for two-variables functions and introduced q 1 q 2 -Simpson-type form inequalities for two-variables functions over finite rectangles.…”

Section: Definition 4 a Function ψmentioning

confidence: 99%

“…For more details on inequalities, we refer the interested reader to [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

et al. 2019

Self Cite

View full text Add to dashboard Cite

In this paper, we present a new definition of higher-order generalized strongly preinvex functions. Moreover, it is observed that the new class of higher-order generalized strongly preinvex functions characterize various new classes as special cases. We acquire a new q 1 q 2 -integral identity, then employing this identity, we establish several two-variable q 1 q 2 -integral inequalities of Simpson-type within a class of higher-order generalized strongly preinvex and quasi-preinvex functions. Finally, the utilities of our numerical approximations have concrete applications.

show abstract

“…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]. Recently, many investigations about (1.1) can be found by Rashid et al [25] for preinvex functions, Li and Du [26] for (α, m)-GA-convex functions, Xi and Qi [27] for logarithmically convex functions, Sarikaya et al [28] for s-convex functions and İşcan et al [29] for p-convex function.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

Self Cite

View full text Add to dashboard Cite

The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

show abstract

Simpson’s type integral inequalities for <em>ĸ</em>-fractional integrals and their applications

Cited by 35 publications

References 8 publications

Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

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

Contact Info

Product

Resources

About