On approximately harmonic h-convex functions depending on a given function

Awan, Muhammad Uzair; Noor, Muhammad Aslam; Mihai, V Marcela; Inayat, Khalida Noor; Akhtar, Nousheen

doi:10.2298/fil1912783a

Cited by 10 publications

(2 citation statements)

References 9 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above denition recapture all denition cited for d (x, y) = 0, strongly harmonic h-convexity, see [25], γ-paraharmonic h-convexity, -paraharmonic h-convexity and relaxed harmonic h-convexity and their subclasses, that is to say convex, s-convex, P -function, Q-functions, s-Q-functions, M T -convex, tgs-convex and beta-convex, see [1]. Denition 1.12.…”

Section: Introductionsupporting

confidence: 54%

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

Meftah¹

2020

matbil

View full text Add to dashboard Cite

In this paper, we present a new denition of preinvex functions depending on the given function which is called as approximately harmonic h-preinvex functions. We establish some inequalities of HermiteHadamard, Simpson and midpoint type for newly dene class of functions. We show that this class contains several other new and known extensions of harmonic preinvexity. Special cases which can be deduced from the main results are also discussed in detail.

show abstract

Section: Introductionsupporting

confidence: 54%

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

Meftah¹

2020

matbil

View full text Add to dashboard Cite

show abstract

“…In literature, there exist many versions of convex functions, for example, h-convex function, see [3], r-convex functions, see [4], harmonic convex function, see [5], exponentially convex functions, see [6], etc. [7,8].…”

Section: Introductionmentioning

confidence: 99%

On Extended Convex Functions via Incomplete Gamma Functions

Zhao

Saleem

Mehmood

et al. 2021

Journal of Function Spaces

View full text Add to dashboard Cite

Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h -exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomplete gamma functions. Precisely speaking, we established trapezoidal, midpoint, and He’s inequalities for h -exponential and harmonically exponential convex functions via incomplete gamma functions. Moreover, we gave several remarks to prove that our results are more generalized than the existing results in the literature.

show abstract

Relative Strongly Exponentially Convex Functions

Noor

Rassias

2020

Springer Optimization and Its Applications

View full text Add to dashboard Cite

On approximately harmonic h-convex functions depending on a given function

Cited by 10 publications

References 9 publications

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

On Extended Convex Functions via Incomplete Gamma Functions

Relative Strongly Exponentially Convex Functions

Contact Info

Product

Resources

About