Trapezoidal (p,q)-Integral Inequalities Related to (η1,η2)-convex Functions with Applications

Klasoom, Humaira; Cho, Minhyung

doi:10.1007/s10773-021-04739-7

Cited by 4 publications

(4 citation statements)

References 15 publications

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“…Furthermore, several articles [28][29][30] have demonstrated fractional trapezoidal-type inequalities for functions with convex second derivatives in the absolute value. Klasoom et al [31,32] examined various modifications of trapezoidal-type inequalities for twice differentiable convex functions using (p,q)-integrals. For different fractional versions of various inequalities, see [33,34].…”

Section: 𝒢(𝜅𝜃 + (1 − 𝜅)𝜆) ≤ 𝜅𝒢(𝜃) + (1 − 𝜅)𝒢(𝜆)mentioning

confidence: 99%

Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane

Alshehry,

Ciurdariu,

Saber

et al. 2024

Axioms

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Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ-pre-invex interval-valued mappings (C·L·R-ℏ-pre-invex Ι·V-M), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte’s type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes.

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Section: 𝒢(𝜅𝜃 + (1 − 𝜅)𝜆) ≤ 𝜅𝒢(𝜃) + (1 − 𝜅)𝒢(𝜆)mentioning

confidence: 99%

Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane

Alshehry,

Ciurdariu,

Saber

et al. 2024

Axioms

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“…The authors Ntouyas and Tariboon [5,6] examined how quantum derivatives and quantum integrals are solved across the intervals of the type [ϕ 1 , ϕ 2 ] ⊂ R in their prior papers, which establish various quantum analogs for several well-known effects, including as the Hölder inequality, the Hermite-Hadamard inequality, and the Ostrowski inequality, as well as Cauchy-Bunyakovsky-Schwarz, Gruss, Gruss-Chebyshev, and other integral inequalities that make use of classical convexity. Research on q-calculus analysis has been conducted by a large number of mathematicians; for more information, the reader may refer to [7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Montgomery Identity and Ostrowski-Type Inequalities for Generalized Quantum Calculus through Convexity and Their Applications

et al. 2022

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The celebrated Montgomery identity has been studied extensively since it was established. We found a novel version of the Montgomery identity when we were working inside the framework of p- and q-calculus. We acquire a Montgomery identity through a definite (p,q)-integral from these results. Consequently, we establish specific Ostrowski-type (p,q)-integral inequalities by using Montgomery identity. In addition to the well-known repercussions, this novel study provides an opportunity to set up new boundaries in the field of comparative literature. The research that is being proposed on the (p,q)-integral includes some fascinating results that demonstrate the superiority and applicability of the findings that have been achieved. This highly successful and valuable strategy is anticipated to create a new venue in the contemporary realm of special relativity and quantum theory. These mathematical inequalities and the approaches that are related to them have applications in the areas that deal with symmetry. Additionally, an application to special means is provided in the conclusion.

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“…Latif et al [22] proved the new variations in trapezoidal inequalities after quantum have been shown to be achieved using the new (p, q)-integral identity. Based on (p, q)-calculus, many works have been published by many researchers, see in [23][24][25][26][27][28][29][30] for more details and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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

Kalsoom

Vivas-Cortez

Latif

2021

Entropy

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Trapezoidal (p,q)-Integral Inequalities Related to (η1,η2)-convex Functions with Applications

Cited by 4 publications

References 15 publications

Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane

Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane

Montgomery Identity and Ostrowski-Type Inequalities for Generalized Quantum Calculus through Convexity and Their Applications

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

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