Integral inequalities for <i>n</i>‐polynomial <i>s</i>‐type preinvex functions with applications

Butt, Saad Ihsan; Budak, Hüseyın; Tariq, Muhammad; Nadeem, Muhammad

doi:10.1002/mma.7465

Cited by 9 publications

(2 citation statements)

References 32 publications

(66 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This better inequality has attracted a large number of authors who have used Hölder–Iscan integral inequality to provide the best technique in the field of integral inequality linked to Hermit–Hadamard inequality [3–5], Jensen inequality [6, 7], Ostrowski inequality [8], Bullen‐type inequality [9], and Simpson inequality [10], such as refinement, generalization, or extension. H ölder–Iscan integral inequality is overused in various

n

‐polynomial convexity [11, 12] and power‐mean integral inequality results [13]. Kadakal et al [13] authors gave a refinement of the power‐mean integral inequality in the following theorem.…”

Section: Introductionmentioning

confidence: 99%

On the refinements of some important inequalities with a finite set of positive numbers

Benaissa,

Zeki Sarikaya

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In this research, a novel method for enhancing the Hölder–Işcan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This approach outperforms traditional Hölder and mean power integral inequalities by employing a finite set of functions. Through the careful selection of the function , an entirely new category of classical inequalities emerges for both Hölder and mean power inequalities.

show abstract

n

Section: Introductionmentioning

confidence: 99%

On the refinements of some important inequalities with a finite set of positive numbers

Benaissa,

Zeki Sarikaya

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…It has been demonstrated by numerous scholars that the characteristics of preinvex functions have useful and relevant applications in the science of mathematical programming and optimization. See references [33,34].…”

Section: Introductionmentioning

confidence: 99%

New Variant of Hermite–Hadamard, Fejér and Pachpatte-Type Inequality and Its Refinements Pertaining to Fractional Integral Operator

2023

Self Cite

View full text Add to dashboard Cite

In order to show novel generalizations of mathematical inequality, fractional integral operators are frequently used. Fractional operators are used to simulate a broad range of scientific as well as engineering phenomena such as elasticity, viscous fluid, fracture mechanics, continuous population, equilibrium, visco-elastic deformation, heat conduction problems, and others. In this manuscript, we introduce some novel notions of generalized preinvexity, namely the (m,tgs)-type s-preinvex function, Godunova–Levin (s,m)-preinvex of the 1st and 2nd kind, and a prequasi m-invex. Furthermore, we explore a new variant of the Hermite–Hadamard (H–H), Fejér, and Pachpatte-type inequality via a generalized fractional integral operator, namely, a non-conformable fractional integral operator (NCFIO). In addition, we explore new equalities. With the help of these equalities, we examine and present several extensions of H–H and Fejér-type inequalities involving a newly introduced concept via NCFIO. Finally, we explore some special means as applications in the aspects of NCFIO. The results and the unique situations offered by this research are novel and significant improvements over previously published findings.

show abstract

Some new (p,q)$$ \left(p,q\right) $$‐Hadamard‐type integral inequalities for the generalized m$$ m $$‐preinvex functions

Kalsoom,

Khan,

Agarwal

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper introduces and establishes new Hermite‐Hadamard type inequalities specifically tailored for ‐preinvex functions within the ‐calculus framework. These newly developed inequalities come with accompanying left‐right estimates, which enhance their practical utility. The primary objective of this research is to investigate the properties of ‐differentiable ‐preinvex functions and derive inequalities that extend and generalize existing results in the domain of integral inequalities. The techniques employed in this study hold broader implications, finding relevance in various fields where symmetry is paramount. The findings presented in this paper make a significant contribution to the field of analytic inequalities, offering valuable insights into the behavior and characteristics of ‐preinvex functions. Moreover, the established results demonstrate the wider applicability and generalization of analogous findings from prior literature. The techniques and inequalities introduced herein pave the way for further exploration and research in the realm of integral inequalities.

show abstract

Integral inequalities for n‐polynomial s‐type preinvex functions with applications

Cited by 9 publications

References 32 publications

On the refinements of some important inequalities with a finite set of positive numbers

On the refinements of some important inequalities with a finite set of positive numbers

New Variant of Hermite–Hadamard, Fejér and Pachpatte-Type Inequality and Its Refinements Pertaining to Fractional Integral Operator

Some new (p,q)$$ \left(p,q\right) $$‐Hadamard‐type integral inequalities for the generalized m$$ m $$‐preinvex functions

Contact Info

Product

Resources

About