In this paper, some integral inequalities of Hermite-Hadamard type for multiplicatively s-convex functions are obtained. Also, some new inequalities involving multiplicative integrals are established ...for product and quotient of convex and multiplicatively s-convex functions.
In this paper, the concept of exponentially -convex stochastic process is introduced. Several new inequalities of Hermite-Hadamard type for exponentially -convex stochastic process are established. ...Some special cases are given which are obtained from our main results. The results obtained in this work are the generalizations of the known results.
In this paper, we introduced the concept of multiplicatively
p
-convex functions and established Hermite-Hadamard type integral inequalities in the setting of multiplicative calculus for this newly ...created class of functions. We also gave integral inequalities of Hermite-Hadamard type for product and quotient of multiplicatively
p
-convex functions. Furthermore, we obtained novel multiplicative integral-based inequalities for the product and quotient of convex and multiplicatively
p
-convex functions. Additionally, we derived certain upper limits for this new class of functions. The findings we proved are generalizations of the results in the literature. The results obtained in this study may inspire further research in various scientific areas.
In this paper, some new inequalities of the Hermite–Hadamard type for the classes of functions whose derivatives’ absolute values are
m
-convex and
(
α
,
m
)
-convex are obtained. The results ...obtained in this work extend and improve the corresponding ones in the literature. Some applications to special means of real numbers are also given.
In this paper, we establish some new integral inequalities of Hermite–Hadamard type for
s
-convex functions by using the Hölder–İşcan integral inequality. We also compare our new results with the ...known results and show that the results which we obtained are better than the known results. Finally, we give some applications to trapezoidal formula and to special means.
We firstly study ∗integrability and commutativity for multiplicative fractional integrals with exponential kernels, proposed by Peng et al. (2022). Secondly, making use of such operators, we present ...a symmetrical multiplicative fractional integrals identity. Based on it, and the fact that the function T∗ is multiplicatively convex or the function (lnT∗)θ is convex for θ>1, especially pondering the case of 0<θ≤1, we establish the symmetrical Hermite–Hadamard type inequalities for multiplicative convexity. We also give some applications in special means under multiplicative calculus.
In the paper, the author introduces a new class of harmonically convex functions, which is called harmonically α,s-convex functions and establishes some new integral inequalities of the ...Hermite-Hadamard type for harmonically α,s-convex functions. The properties of the newly introduced class of harmonically convex functions are also investigated. Finally, some applications to special means are given.
In this work, the notion of a multiplicative harmonic convex function is examined, and Hermite–Hadamard inequalities for this class of functions are established. Many inequalities of Hermite–Hadamard ...type are also taken into account for the product and quotient of multiplicative harmonic convex functions. In addition, new multiplicative integral-based inequalities are found for the quotient and product of multiplicative harmonic convex and harmonic convex functions. In addition, we provide certain upper limits for such classes of functions. The obtained results have been verified by providing examples with included graphs. The findings of this study may encourage more research in several scientific areas.
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