Hadamard and Fejér-Hadamard inequalities for generalized $ k $-fractional integrals involving further extension of Mittag-Leffler function

Self Cite

In this article, generalized versions of the k -fractional Hadamard and Fejér-Hadamard inequalities are constructed. To obtain the generalized versions of these inequalities, k -fractional integral operators including the well-known Mittag-Leffler function are utilized. The class of ( p , h )-convex functions for Hadamard-type inequalities give the generalizations of results which have been proved in literature for p -convex, h -convex, and several functions deducible from these two classes.

“…Lemma 15 (see [18]). Let σ, ς : ½ε, υ ⟶ ℝ with 0 < ε < υ be the functions such that σ is positive and σ ∈ L 1 ½ε, υ, and ς is differentiable and absolutely increasing.…”

Section: K-fractional Integral Inequalities Of Hadamard and Fejér-had...mentioning

confidence: 99%

“…Recently, Yue et al [18] described generalized k-fractional operators including the further extension of the Mittag-Leffler function as noted below.…”

Section: Introductionmentioning

confidence: 99%

( $p, h$ )-Convex Functions Associated with Hadamard and Fejér-Hadamard Inequalities via $k$ -Fractional Integral Operators

Zhang

Farid

Demirel

et al. 2022

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“…Since the classical convexity is not enough to attain certain goals in applied mathematics, so the classical convexity has been generalized in many directions. For recent generalizations, one can see [5,6].…”

Section: Introductionmentioning

confidence: 99%

Fractional Version of Hermite-Hadamard and Fejér Type Inequalities for a Generalized Class of Convex Functions

Geng

Saleem

Aslam

et al. 2022

In the present paper, we deal with some fractional integral inequalities for strongly reciprocally p , h -convex functions. We established fractional version of Hermite-Hadamard and Fejér type inequalities for strongly reciprocally p , h -convex functions. Our results extend and generalize many exiting results of literate.

“…Moreover, we develop some fractional integral inequalities. See [7,8] for more general inequalities via convexity of functions.…”

Section: Introductionmentioning

confidence: 99%

Fractional Versions of Hermite-Hadamard, Fejér, and Schur Type Inequalities for Strongly Nonconvex Functions

Muhammad

Yasin

et al. 2022

In modern world, most of the optimization problems are nonconvex which are neither convex nor concave. The objective of this research is to study a class of nonconvex functions, namely, strongly nonconvex functions. We establish inequalities of Hermite-Hadamard and Fejér type for strongly nonconvex functions in generalized sense. Moreover, we establish some fractional integral inequalities for strongly nonconvex functions in generalized sense in the setting of Riemann-Liouville integral operators.