Monotonicity of sequences involving geometric means of positive sequences with monotonicity and logarithmical convexity
نویسندگان
چکیده
منابع مشابه
Monotonicity of Sequences Involving Convex and Concave Functions
Let f be an increasing and convex (concave) function on [0, 1) and φ a positive increasing concave function on [0,∞) such that φ(0) = 0 and the sequence { φ(i+1) ( φ(i+1) φ(i) − 1 )} i∈N decreases ( the sequence { φ(i) ( φ(i) φ(i+1) − 1 )} i∈N increases ) . Then the sequence { 1 φ(n) ∑n−1 i=0 f ( φ(i) φ(n) )} n∈N is increasing. Mathematics subject classification (2000): 26D15, 26A51.
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2006
ISSN: 1331-4343
DOI: 10.7153/mia-09-01