Functional inequalities for the incomplete gamma function
Copyright policy )Functional inequalities for the incomplete gamma function
Let \(f_a(x)= \Gamma(a,x)/\Gamma(a,0)\), where \(\Gamma(a,x)\) denotes the incomplete gamma function \((a,x> 0)\). The authors prove various new functional inequalities for \(f_a(x)\). For example, they study the double inequality \[ f_a(S_p(x_1,\dots, x_n))\leq f_a(x_1)\cdots f_a(x_n)\leq f_a(S_q(x_1,\dots, x_n)), \] where \(S_t\) is the power sum of order \(t\). They also prove that \(f_a(x)\) is completely monotonic on \([0,\infty)\) iff \(a\in(0,1]\) and provide all parameters \(b\), \(c\) such that the function \(g(x)= [f_a(x^b)]^c\) is subadditive on \([0,\infty)\).
- Babeș-Bolyai University Romania
Subadditive, Completely monotonic, Arithmetic, geometric, and harmonic means, incomplete gamma function, power sums, Power means, functional inequalities, Turán-type inequality, power means, and harmonic means, completely monotonic, Applied Mathematics, Functional inequalities, convex, concave, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), Convex, arithmetic, Incomplete gamma function, Grünbaum-type inequality, Power sums, geometric, Inequalities for sums, series and integrals, subadditive, Concave, Analysis
Subadditive, Completely monotonic, Arithmetic, geometric, and harmonic means, incomplete gamma function, power sums, Power means, functional inequalities, Turán-type inequality, power means, and harmonic means, completely monotonic, Applied Mathematics, Functional inequalities, convex, concave, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), Convex, arithmetic, Incomplete gamma function, Grünbaum-type inequality, Power sums, geometric, Inequalities for sums, series and integrals, subadditive, Concave, Analysis
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