Some Inequalities for Operator (<i>p</i>, <i>h</i>)‐Convex Function

Omrani, Zahra; Rahpeyma, Omid Pourbahri; Rahimi, Hamidreza

doi:10.1155/2022/3836837

Cited by 4 publications

(3 citation statements)

References 22 publications

(22 reference statements)

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“…Hu et al [15] proposed several inequalities for a new category of convex functions, as well as implications involving the local fractional integral. Omrani et al [16] created a Hermite-Hadamard inequality for (p, h)-convex functions and also introduced this class. Zhao et al [17] inaugurated two crucial right q-integral equalities containing a right-quantum derivative with parameter m ∈ [0, 1] and then derives some novel variants for midpoint and trapezoid-type inequalities for the right-quantum integral via differentiable (𝛼, m)-convex functions.…”

Section: Introductionmentioning

confidence: 99%

Error estimates of Hermite‐Hadamard type inequalities with respect to a monotonically increasing function

Samraiz

Malik

Naheed

et al. 2023

Math Methods in App Sciences

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Fractional calculus is used to examine and enhance the concept of calculus in diverse fields of science. In this paper, we establish Hermite‐Hadamard inequalities for composite ‐convex function. The generalized identities are established for Riemann‐type fractional integrals. The explored identities are used to examine error estimates of Hermite‐Hadamard inequalities for ‐convex function concerning a strictly monotone function. Some results that exist in literature are obtained as special cases to our general results. The conclusions of this article may be useful in determining the uniqueness of partial differential equations and fractional boundary value problems.

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Section: Introductionmentioning

confidence: 99%

Error estimates of Hermite‐Hadamard type inequalities with respect to a monotonically increasing function

Samraiz

Malik

Naheed

et al. 2023

Math Methods in App Sciences

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“…The following inequalities due to authors [13], give the Hermite-Hadamard inequality for operator (p, h)-convex functions.…”

Section: Introductionmentioning

confidence: 99%

Some trace functional inequalities for‎ ‎operator (p‎, ‎h)-convex functions

Rahpeyma,

Bakan,

Bodaghi

2023

Preprint

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“…In 2017, Wang and Sun [7] established the Hermite-Hadamard-type inequalities for operator α-preinvex functions. In 2022, Omrani et al [9] proposed the Hermite-Hadamard-type inequalities for operator (p, h)-convex functions.…”

Section: Introductionmentioning

confidence: 99%

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

Mehmood

Srivástava

Mohammed

et al. 2022

Axioms

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In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator ω1,ω2-preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator ω1,ω2-preinvex functions of the positive self-adjoint operator in the complex Hilbert spaces. We give the special cases to our results; thus, the established results are generalizations of earlier work. In the last section, we give applications for synchronous (asynchronous) functions.

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Some Inequalities for Operator (p, h)‐Convex Function

Abstract: In this paper, we introduce operator p , h -convex functions and establish a Hermite–Hadamard inequality for these functions. As application, we obtain several trace and singular value inequalities of operators.

Cited by 4 publications

References 22 publications

Error estimates of Hermite‐Hadamard type inequalities with respect to a monotonically increasing function

Error estimates of Hermite‐Hadamard type inequalities with respect to a monotonically increasing function

Some trace functional inequalities for‎ ‎operator (p‎, ‎h)-convex functions

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

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