On the bounds for the normalized Jensen functional and Jensen-Steffensen inequality
نویسندگان
چکیده
منابع مشابه
Bounds for the Normalized Jensen – Mercer Functional
We introduce the normalized Jensen-Mercer functional Mn( f ,x, p) = f (a)+ f (b)− n ∑ i=1 pi f (xi)− f ( a+b− n ∑ i=1 pixi ) and establish the inequalities of type MMn( f ,x,q) Mn( f ,x, p) mMn( f ,x,q) , where f is a convex function, x = (x1, . . . ,xn) and m and M are real numbers satisfying certain conditions. We prove them for the case when p and q are nonnegative n -tuples and when p and q...
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* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, 68-b, New Muslim Town, Lahore 54600, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we extend some old and give some new refinements of the JensenSteffensen inequality. Further, we investigate the log-convexity and the exponential conve...
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New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen’s inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon’s inequality and the positivity of Kullback-Leibler divergence are obtained.
متن کاملNormalized Jensen Functional, Superquadracity and Related Inequalities
In this paper we generalize the inequality MJn (f,x,q) ≥ Jn (f,x,p) ≥ mJn (f,x,q) where Jn (f,x,p) = n ∑ i=1 pif (xi)− f ( n ∑ i=1 pixi ) , obtained by S.S. Dragomir for convex functions. We provide cases where we can improve the bounds m and M for convex functions, and also, we show that for the class of superquadratic functions nonzero lower bounds of Jn (f,x,p)− mJn (f,x,q) and nonzero upper...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2009
ISSN: 1331-4343
DOI: 10.7153/mia-12-32