Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus

Kalsoom, Humaira; Vivas-Cortez, Miguel; Latif, Muhammad Amer

doi:10.3390/e23101238

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…Definition 3. Kalsoom et all [46] and Ion [47] said that a function Ψ : I → R with the modulus c is strongly quasi-convex function, if…”

Section: Discussionmentioning

confidence: 99%

New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities

Ciurdariu,

Grecu

2023

Symmetry

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The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second quantum derivatives in absolute values follow different type of convexities. A new quantum integral identity is derived for twice quantum differentiable functions, which is used as a key element in our demonstrations along with several basic inequalities such as: power mean inequality, and Holder’s inequality. The symmetry of the Hermite-Hadamard type inequalities is stressed by the different types of convexities. Several special cases of the parameter are chosen to illustrate the investigated results. Four examples are presented.

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“…Definition 3. Kalsoom et all [46] and Ion [47] said that a function Ψ : I → R with the modulus c is strongly quasi-convex function, if…”

Section: Discussionmentioning

confidence: 99%

New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities

Ciurdariu,

Grecu

2023

Symmetry

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“…Utilizing an unique integral identity with (p, q)-differentiable functions, Latif et al [21] discovered some new forms of post-quantum trapezoid type inequalities that were previously unknown. Using (α, m)-convex mappings, Humaira et al [22] established the idea of (p, q)-estimates for distinct types of integral inequalities, for more details see in [23][24][25][26][27][28] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

New Parameterized Inequalities for η-Quasiconvex Functions via (p, q)-Calculus

Kalsoom

Vivas-Cortez

Idrees

et al. 2021

Entropy

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In this work, first, we consider novel parameterized identities for the left and right part of the (p,q)-analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized (p,q)-trapezoid and parameterized (p,q)-midpoint type integral inequalities via η-quasiconvex function. By changing values of parameter μ∈[0,1], some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the η-quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained.

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