Results 1 to 10 of about 708 (139)
An accurate approximation formula for gamma function. [PDF]
J Inequal Appl, 2018 In this paper, we present a very accurate approximation for gamma function: \begin{equation*} \Gamma \left( x+1\right) \thicksim \sqrt{2\pi x}\left( \dfrac{x}{e}\right) ^{x}\left( x\sinh \frac{1}{x}\right) ^{x/2}\exp \left( \frac{7}{324}\frac{1}{ x^{3 ...
Yang ZH, Tian JF.
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Strong m-Convexity of Set-Valued Functions
Annales Mathematicae Silesianae, 2023 In this research we introduce the concept of strong m-convexity for set-valued functions defined on m-convex subsets of real linear normed spaces, a variety of properties and examples of these functions are shown, an inclusion of Jensen type is also ...
Lara Teodoro +3 more
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Ohlin and Levin–Stečkin-Type Results for Strongly Convex Functions
Annales Mathematicae Silesianae, 2020 Counterparts of the Ohlin and Levin–Stečkin theorems for strongly convex functions are proved. An application of these results to obtain some known inequalities related with strongly convex functions in an alternative and unified way is presented.
Nikodem Kazimierz, Rajba Teresa
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m-Convex Functions of Higher Order
Annales Mathematicae Silesianae, 2020 In this research we introduce the concept of m-convex function of higher order by means of the so called m-divided difference; elementary properties of this type of functions are exhibited and some examples are provided.
Lara Teodoro +2 more
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Open Mathematics, 2022 In this study, we establish some new Hermite-Hadamard type inequalities for s-convex functions in the second sense using the post-quantum calculus. Moreover, we prove a new (p,q)\left(p,q)-integral identity to prove some new Ostrowski type inequalities ...
You Xue-Xiao +4 more
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Jensen-type inequalities for m-convex functions
Open Mathematics, 2022 Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the main role in the study of the existence and uniqueness of initial and boundary value problems for ...
Bosch Paul +3 more
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A Characterization of Convex Functions [PDF]
, 2017 Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\to \mathbf{R}\cup \{+\infty\}$ is convex if and only if for all $x,y \in D$ there exists $\alpha=\alpha(x,y) \in (0,1)$ such that $f(\alpha
Leonetti, Paolo
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Geometric convexity of the generalized sine and the generalized hyperbolic sine [PDF]
, 2013 In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively.
Jiang, Wei-Dong, Qi, Feng
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Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions
Open Mathematics, 2021 In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by ...
Budak Huseyin +4 more
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New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings
Open Mathematics, 2020 In the article, we present a new (p,q)(p,q)-integral identity for the first-order (p,q)(p,q)-differentiable functions and establish several new (p,q)(p,q)-quantum error estimations for various integral inequalities via (α,m)(\alpha ,m)-convexity. We also
Kalsoom Humaira +4 more
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