Characterizations of Higher Order Strongly Generalized Convex Functions

Noor, Muhammad Aslam; Noor, Khalida İnayat; Rassias, Michael Th.

doi:10.1007/978-3-030-72563-1_15

Cited by 4 publications

(1 citation statement)

References 31 publications

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“…The H-H type integral inequalities are involved in fractional calculus models and they has been applied for different types of convex functions such as MT-type [12], λ ψ -type [14], a new class of convex functions [15], and the readers can find out the other types in the literature [16][17][18].…”

Section: Definition 6 ([12]mentioning

confidence: 99%

Inequalities for m-polynomial exponentially s-type convex functions in fractional calculus

Mohammed¹,

Kashuri²,

Abdalla³

et al. 2023

ScienceAsia

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In this article, we introduce a new class of functions named the m-polynomial exponentially s-type convex and we study some of its algebraic properties. We investigate a new integral inequality of Hermite-Hadamard (H-H) type by using the new introduced definition. Also, we prove a new midpoint identity. By examining this identity we can deduce some integral inequalities of midpoint type for the new introduced definition. Several special cases are discussed in details which emphasize that the results accounted in this paper unify and extend various results in this field of study. Finally, we provide some applications on the Bessel functions and special means of distinct positive real numbers to demonstrate the applicability of the new results.

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Section: Definition 6 ([12]mentioning

confidence: 99%

Inequalities for m-polynomial exponentially s-type convex functions in fractional calculus

Mohammed¹,

Kashuri²,

Abdalla³

et al. 2023

ScienceAsia

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New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

Fahad,

Ali,

Furuichi

et al. 2024

Fractal Fract

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We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs). The two generalized fractional integral operators (FIOs) are Hadamard proportional fractional integral operators (HPFIOs) and Hadamard k-fractional integral operators (HKFIOs). Moreover, we also present the results for subclasses of GA-h-CFs and show that the inequalities proved in this paper unify the results from the recent related literature. Furthermore, we compare the two generalizations in view of the fractional operator parameters that contribute to the generalizations of the results and assess the better approximation via graphical tools. Finally, we present applications of the new inequalities via HPFIOs and HKFIOs by establishing interpolation relations between arithmetic mean and geometric mean and by proving the new upper bounds for the Tsallis relative operator entropy.

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Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus

et al. 2022

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In interval analysis, the fuzzy inclusion relation and the fuzzy order relation are two different concepts. Under the inclusion connection, convexity and non-convexity form a substantial link with various types of inequalities. Moreover, convex fuzzy-interval-valued functions are well known in convex theory because they allow us to infer more exact inequalities than convex functions. Most likely, integral operators play significant roles to define different types of inequalities. In this paper, we have successfully introduced the Riemann–Liouville fractional integrals on coordinates via fuzzy-interval-valued functions (FIVFs). Then, with the help of these integrals, some fuzzy fractional Hermite–Hadamard-type integral inequalities are also derived for the introduced coordinated convex FIVFs via a fuzzy order relation (FOR). This FOR is defined by -cuts or level-wise by using the Kulish–Miranker order relation. Moreover, some related fuzzy fractional Hermite–Hadamard-type integral inequalities are also obtained for the product of two coordinated convex fuzzy-interval-valued functions. The main results of this paper are the generalization of several known results.

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Characterizations of Higher Order Strongly Generalized Convex Functions

Cited by 4 publications

References 31 publications

Inequalities for m-polynomial exponentially s-type convex functions in fractional calculus

Inequalities for m-polynomial exponentially s-type convex functions in fractional calculus

New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus

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