Investigation of a Stolarsky Type Inequality for Integrals in Pseudo-analysis
نویسندگان
چکیده
In this paper, we prove a Stolarsky type inequality for pseudo-integrals. More precisely, we show that: ∫ sup [0,1] f(x 1 a+b )dx ≥ ( ∫ sup [0,1] f(x 1 a )dx ) ̄ ( ∫ sup [0,1] f(x 1 b )dx ) , where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly decreasing function ( strictly increasing function ) and μ is the sup-measure the same as Theorem 2.4. Also ̄ is represented by an increasing multiplicative generator g. MSC 2010: 03E72, 26E50, 28E10
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