New Hermite-Hadamard-Fejér type inequalities for (η1, η2)-convex functions via fractional calculus

Mehmood, Sikander; Zafar, Fiza; Yasmin, Nusrat

doi:10.2306/scienceasia1513-1874.2020.012

Cited by 10 publications

(5 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existing versions of HHF integral inequalities ( 7) and ( 8) have been successfully applied to other classes of convex functions, see [46][47][48]. Therefore, our present results can be applied to those classes of convex functions as well.…”

Section: Discussionmentioning

confidence: 85%

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

et al. 2021

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

Section: Discussionmentioning

confidence: 85%

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

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In our present investigation, we have established new fractional HHF integral inequalities involving the weighted fractional operators associated with positive symmetric functions. The HHF fractional integral inequality (7) has been applied to other class of convex functions, such as p-convex functions [39], generalized convex functions [40], (η 1 , η 2 )-convex functions [41] and many others that can be found in the literature. Thus, the results obtained here can be also be applied to the above class of convex functions.…”

Section: Discussionmentioning

confidence: 99%

Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

2020

View full text Add to dashboard Cite

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

show abstract

“…During the last few decades, most of the scientists have worked to obtain the generalized versions of well-known inequalities and discussed a huge number of applications in the fields of analysis and discrete optimization. Many authors have worked extensively [4][5][6][7][8][9][10][11][12] and discussed the refinements and extensions in different areas of mathematics. The advanced analysis of inequalities is possible for the development of fractional operators by means of their kernel in multi-dimension functions, which play an ideal role to create new horizons to study the behavior of inequalities in multi-discipline branches of mathematics.…”

Section: Introductionmentioning

confidence: 99%

Certain Novel Fractional Integral Inequalities via Fuzzy Interval Valued Functions

Vivas-Cortez,

Ali,

Saif

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

Fuzzy-interval valued functions (FIVFs) are the generalization of interval valued and real valued functions, which have a great contribution to resolve the problems arising in the theory of interval analysis. In this article, we elaborate the convexities and pre-invexities in aspects of FIVFs and investigate the existence of fuzzy fractional integral operators (FFIOs) having a generalized Bessel–Maitland function as their kernel. Using the class of convexities and pre-invexities FIVFs, we prove some Hermite–Hadamard (H-H) and trapezoid-type inequalities by the implementation of FFIOs. Additionally, we obtain other well known inequalities having significant behavior in the field of fuzzy interval analysis.

show abstract

New Hermite-Hadamard-Fejér type inequalities for (η1, η2)-convex functions via fractional calculus

Cited by 10 publications

References 6 publications

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

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

Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Certain Novel Fractional Integral Inequalities via Fuzzy Interval Valued Functions

Contact Info

Product

Resources

About