New Estimates on Hermite-Hadamard Type Inequalities via Generalized Tempered Fractional Integrals for Convex Functions with Applications

Article Multidisciplinary Sciences

Some New Hermite-Hadamard Type Inequalities Pertaining to Fractional Integrals with an Exponential Kernel for Subadditive Functions

Artion Kashuri et al.

Summary: The class of symmetric function interacts extensively with other types of functions, particularly with convex functions. This paper presents new fractional Hermite-Hadamard inequalities with an exponential kernel for subadditive functions and their product, and it also recaptures some known results. Additionally, by using a new identity as an auxiliary result, several inequalities for subadditive functions involving new fractional integrals with an exponential kernel are deduced. The accuracy of the results is validated through examples and graphical representations of suitable choices of subadditive functions.

SYMMETRY-BASEL (2023)

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Article Mathematics, Applied

Some New Jensen-Mercer Type Integral Inequalities via Fractional Operators

Bahtiyar Bayraktar et al.

Summary: In this study, new variants of the Hermite-Hadamard inequality are introduced through non-conformable fractional integrals. These inequalities are applicable to convex functions and differentiable functions with generally convex absolute values of their derivatives. The main results are established using the classical Jensen-Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to confirming known results in the literature, examples of their application are also provided.

AXIOMS (2023)

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Article Mathematics, Applied

Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

Asfand Fahad et al.

Summary: In this paper, a new auxiliary identity of the Bullen type is established for twice-differentiable functions using fractional integral operators. Based on this new identity, generalized Bullen-type inequalities are derived by exploiting convexity properties. Concrete examples are provided to illustrate the results, and their correctness is confirmed through graphical analysis. Estimations of bounds are analyzed, showing that improved Holder and power mean inequalities yield better upper-bound results compared to classical inequalities. Furthermore, applications to quadrature rules, modified Bessel functions, and digamma functions are discussed.

AXIOMS (2023)

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Article Mathematics

Refinement Mappings Related to Hermite-Hadamard Type Inequalities for GA-Convex Function

Muhammad Amer Latif et al.

Summary: In this paper, we introduce new refinement mappings associated with the Hermite-Hadamard type inequalities for GA-convex mappings. Our investigation uncovers interesting features and develops inequalities for the Hermite-Hadamard type inequalities that have already been established for GA-convex functions. Furthermore, we refine the relationship between the middle, rightmost, and leftmost elements of the function. Additionally, we provide applications to special means of positive real numbers.

MATHEMATICS (2022)

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Article Mathematics, Applied

Inequalities of Simpson-Mercer-type including Atangana-Baleanu fractional operators and their applications

Muhammad Tariq et al.

Summary: This article discusses new variants of Simpson-Mercer type inequalities involving the Atangana-Baleanu (A-B) fractional integral operator for s-convex functions. Several applications are studied to confirm the effectiveness and validity of the results.

AIMS MATHEMATICS (2022)

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Article Mathematics, Applied

Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application

Soubhagya Kumar Sahoo et al.

Summary: Defining new fractional operators and employing them to establish well-known integral inequalities has become a recent trend in mathematical inequality theory. In this paper, novel versions of Hermite-Hadamard type inequalities for a new fractional operator are presented. Furthermore, a midpoint type fractional integral identity is derived for differentiable mappings with convex absolute value of the first-order derivatives. Several improved inequalities are also derived using fundamental inequalities such as Holder-Iscan, Jensen, and Young inequality, with the derived identity as an auxiliary result. Additionally, new results for Atangana-Baleanu equivalence are obtained by setting the parameter rho to be 1 in most of the results. An application example related to matrices is also provided.

AIMS MATHEMATICS (2022)

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Article Multidisciplinary Sciences