Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

Han, Jiangfeng; Mohammed, Pshtiwan Othman; Zeng, Huidan

doi:10.1515/math-2020-0038

Cited by 68 publications

(33 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assume that Υ : [u, v] ⊆ R → R is an L 1 integrableσ-convex function and Υ ∈ L 1 (u, v) with 0 ≤ u < v. If the functionσ is increasing and positive on (u, v] andσ (x) is continuous on (u, v). Then, we have (20) for ℘ > 0.…”

Section: Proof By Definition 3 and Integrating By Parts One Can Findmentioning

confidence: 99%

See 1 more Smart Citation

Fractional Hermite-Hadamard Integral Inequalities for a New Class of Convex Functions

et al. 2020

Self Cite

View full text Add to dashboard Cite

Fractional integral inequality plays a significant role in pure and applied mathematics fields. It aims to develop and extend various mathematical methods. Therefore, nowadays we need to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of the fractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integral inequalities due to the behavior of its definition and properties. There is also a strong relationship between convexity and symmetric theories. So, whichever one we work on, we can then apply it to the other one due to the strong correlation produced between them, specifically in the last few decades. First, we recall the definition of φ-Riemann–Liouville fractional integral operators and the recently defined class of convex functions, namely the σ˘-convex functions. Based on these, we will obtain few integral inequalities of Hermite–Hadamard’s type for a σ˘-convex function with respect to an increasing function involving the φ-Riemann–Liouville fractional integral operator. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities. Finally, application to certain special functions are pointed out.

show abstract

Section: Proof By Definition 3 and Integrating By Parts One Can Findmentioning

confidence: 99%

“…After introducing Hermite-Hadamard type inequalities (2) and (3), many classical and fractional integral inequalities have been established by a huge number of researcher; for more details one can see References [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Fractional Hermite-Hadamard Integral Inequalities for a New Class of Convex Functions

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, the endpoint HH inequality (3) has been applied for various classes of convexity such as λ ψ -convexity [26], F-convexity [27], (α, m)-convexity [28], MT-convexity [29]. The reader can find other types of convexity in the literature, which in particular, is true for [30].…”

Section: Introductionmentioning

confidence: 99%

Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry Function Kernels

et al. 2021

Self Cite

View full text Add to dashboard Cite

The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.

show abstract

“…In [13], Ertuğral and Sarikaya presented some Simpson type inequalities for these fractional integral operators. For some of other papers on inequalities for generalized fractional integrals, we refer to [17,48]. On the other hand, Turkay et al described the generalized fractional integrals for functions with two variables.…”

Section: Introductionmentioning

confidence: 99%

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

2021

View full text Add to dashboard Cite

In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane $\mathbb{R} ^{2}$ R 2 . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

show abstract

Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

Cited by 68 publications

References 32 publications

Fractional Hermite-Hadamard Integral Inequalities for a New Class of Convex Functions

Fractional Hermite-Hadamard Integral Inequalities for a New Class of Convex Functions

Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry Function Kernels

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

Contact Info

Product

Resources

About