Some Hermite‐Hadamard's type local fractional integral inequalities for generalized γ‐preinvex function with applications

Al-Sa’di, Sa’ud; Bibi, Maria; Muddassar, Muhammad

doi:10.1002/mma.8680

Cited by 12 publications

(3 citation statements)

References 38 publications

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“…Jain et al [25] developed some new quantum variants of Saigo-type fractional operators and studied well-known inequalities by employing these operators. For further reading, interested readers can refer to [26][27][28][29][30][31][32][33].…”

Section: Definition 4 ([8]mentioning

confidence: 99%

Exploration of Quantum Milne–Mercer-Type Inequalities with Applications

et al. 2023

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Quantum calculus provides a significant generalization of classical concepts and overcomes the limitations of classical calculus in tackling non-differentiable functions. Implementing the q-concepts to obtain fresh variants of classical outcomes is a very intriguing aspect of research in mathematical analysis. The objective of this article is to establish novel Milne-type integral inequalities through the utilization of the Mercer inequality for q-differentiable convex mappings. In order to accomplish this task, we begin by demonstrating a new quantum identity of the Milne type linked to left and right q derivatives. This serves as a supporting result for our primary findings. Our approach involves using the q-equality, well-known inequalities, and convex mappings to obtain new error bounds of the Milne–Mercer type. We also provide some special cases, numerical examples, and graphical analysis to evaluate the efficacy of our results. To the best of our knowledge, this is the first article to focus on quantum Milne–Mercer-type inequalities and we hope that our methods and findings inspire readers to conduct further investigation into this problem.

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Section: Definition 4 ([8]mentioning

confidence: 99%

Exploration of Quantum Milne–Mercer-Type Inequalities with Applications

et al. 2023

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“…Ohud Almutairi [1] studied the concept of generalized (h − m)convexity in the frame work of fractal sets and established generalized Fejér-Hermite-Hadamard type inequalities through this notion of convex functions. Al-Sa'di et al [2] introduced the γ-preinvex function and derived a number of generalized Hermite-Hadamard type inequalities. Wenbing Sun discussed various generalizations of convex functions in the fractal theory in references [26,[28][29][30]39].…”

Section: Introductionmentioning

confidence: 99%

Generalized m -preinvexity on fractal set and related local fractional integral inequalities with applications

AL-SA’DI¹,

Bibi²,

Muddassar³

et al. 2023

J. Math. Computer Sci.

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In this work, we address and explore the concept of generalized m-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate the current initiated idea. Furthermore, we prove the latest variant of Hermite-Hadamard type inequality employing the proposed definition of preinvexity. We also derive several novel versions of inequalities of the Hermite-Hadamard type and Fejér-Hermite-Hadamard type for the first-order local differentiable generalized m-preinvex functions. Finally, some new inequalities for the generalized means and generalized random variables are established as applications.

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“…Certain generalized Pompeiutype integral inequalities and its applications were discussed by Erden and Sarikaya [10]. In [4], Al-Sa'di et al investigated the generalized γ-preinvex mappings and established several generalizations of Hermite-Hadamard type inequalities. Making use of local fractional integrals and generalized (h, m)-convexity, the Hermite-Hadamard-and Fejér-Hermite-Hadamard-type inequalities were generalized by Almutairi and Kilic ¸man [3], and they also derived certain integral inequalities involving generalized s-convexity through Katugampola fractional integrals on fractal sets [2].…”

Section: Introduction-preliminariesmentioning

confidence: 99%

Error bounds on the Hermite-Hadamard- and Bullen-type inequalities for $2\alpha$-local fractional derivative

2023

J. Nonlinear Funct. Anal.

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We present a general integral identity involving 2α-local fractional derivative. Based on the integral identity and the fact that the 2α-local fractional derivative in absolute value is generalized (s, P)-convex, we establish certain integral inequalities that cover each case of the generalized Hermite-Hadamard's and Bullen type for the class of mappings. Certain applications in α-type special means, probability distribution mappings, the trapezoidal and midpoint formulas, and wave equations on Cantor sets are presented to demonstrate the validity of the obtained results as well.

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Some Hermite‐Hadamard's type local fractional integral inequalities for generalized γ‐preinvex function with applications

Cited by 12 publications

References 38 publications

Exploration of Quantum Milne–Mercer-Type Inequalities with Applications

Exploration of Quantum Milne–Mercer-Type Inequalities with Applications

Generalized m -preinvexity on fractal set and related local fractional integral inequalities with applications

Error bounds on the Hermite-Hadamard- and Bullen-type inequalities for $2\alpha$-local fractional derivative

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