Log-Convex Functions
The Choquet integral of log convex functions
... for log-convex functions. Firstly, for a monotone log-convex function, we state the similar Hadamard inequality of the Choquet integral in the framework of distorted ...general ...
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The Sugeno fuzzy integral of log convex functions
... In this paper, we give an upper bound for the Sugeno fuzzy integral of log-convex functions using the classical Hadamard integral inequality. We present a geometric interpretation and some examples ...
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Refinements of the Hermite-Hadamard Integral Inequality for Log-Convex Functions
... where G (p, q) := √ pq is the geometric mean and L (p, q) := ln p p − − q ln q (p 6 = q) is the logarithmic mean of the positive real numbers p, q (for p = q, we put L (p, p) = p). In this paper we prove another ...
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Further inequalities for log-convex functions related to Hermite-Hadamard result
... [44] E. K. Godunova and V. I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of func- tions. (Russian) Numerical mathematics and mathematical physics ...
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New Inequalities of Hermite-Hadamard Type for Log-Convex Functions
... 42. E.K. Godunova and V.I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (Russian) Numerical mathematics and mathematical ...
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A Class of k-Log-Convex Functions and their Applications to Some Special Functions
... Before verifying Theorem 1 and Theorem 2, we would like to apply them to de- duce some known and new conclusions related to some special functions such as the gamma function, Riemann’s zeta function, complete ...
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Fractional Hermite-Hadamard type inequalities for n-times log-convex functions
... The main purpose of this paper is to establishing a new Hermite–Hadamard type inequalities for functions whose n th derivatives are logarithmically convex and via Riemann–Liouville integ[r] ...
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On The Hadamard's Inequality for Log Convex Functions on the Coordinates
... The maximum modulus principle in complex analysis states that if f is a holomorphic function, then the modulus |f| cannot exhibit a true local maximum that is properly within the domain of f. Characterizations of the ...
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Refinements to Hadamard’s Inequality for Log Convex Functions
... Sulaiman Department of Computer Engineering, College of Engineering, University of Mosul, Mosul, Iraq E-mail: [email protected] Received April 25, 2011; revised May 25, 2011; acce[r] ...
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n-Exponential convexity for Favard's and Berwald's inequalities and their applications
... is log-convex in the Jensen- sense if and only if it is 2-exponentially convex in the Jensen ...is log-convex if and only if it is 2-exponentially ...If convex functions ...
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On the Hermite-Hadamard Inequality and Other Integral Inequalities Involving Two Functions
... two convex and log-convex functions, ...m)-convex functions. In [10], analogous results for s-convex functions were proved by Kırmacı, Bakula, ¨ Ozdemir and Peˇ ...
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Certain geometric properties of Mittag Leffler functions
... real functions T was intro- duced by Robertson ...be convex in the direction of imaginary axis if and only if the domain f (U ) is convex in the direction of imaginary ...
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MetaGrad: Multiple Learning Rates in Online Learning
... This partitions OCO tasks into categories, leaving it to the user to choose the appropriate algorithm for their setting. Such a strict partition, apart from being a burden on the user, depends on an extensive cataloguing ...
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A note on generalized convex functions
... not convex, prove that every η-convex function defined on rectangle is coordinate η-convex but not vice versa, define the coordinate (η 1 , η 2 ...
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Spiral like integral operators
... and Mehrok, T.J.S.: On Univalence of certain analytic functions associated wih starlike, convex and close-to-convex functions, Indian J.. BERNARDI, S.D.: Convex and starlike univalent fu[r] ...
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Extension of Stolarsky means by Euler-Radau expansions
... Here we list some families of functions F = { f t : t ∈ I} from [7] for which we will use Corollaries 1.14 and 1.15 in order to construct exponentially convex functions and then means. Of course, we ...
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On ε-optimality conditions for multiobjective fractional optimization problems
... objective functions with convex numerator functions and convex denominator functions, finitely many convex constraint functions, and a geometric constraint set, is ...
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Analytic Functions Related with Mocanu Class
... where its geometric definition and connections with the conic domains were considered. It is worth mentioning that 1 − U CV = U CV. In recent years many authors investigated interesting properties of these classes. For ...
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On Certain Classes of Convex Functions
... for functions in bounded positive class K(𝛼, ...for functions in the ...inverse functions and bi- univalent ...of functions in special subclasses of S, the readers may be referred to the works ...
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Certain convex harmonic functions
... Notice that if g ≡ 0 and α = 0 then the family ᏴᏯᐂ (k,α) defined by (1.7) reduces to the class k- ᐁᏯᐂ of k-uniformly convex analytic functions defined by (1.5). If we, further, let k = 1 in (1.5), we obtain ...
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