设:f(x)∈AC[o,A),并f(0)＝f(h)＝0.则有integral from n=0 to h(|f(x)f(x)|dx)≤h/4 integral from n=0 to h(|f'(x)|~2dx)这个不等式叫做Opial不等式.许多数学家对它曾进行过研究.在此我们给予有意义的改进:integral from n=0 to ...设:f(x)∈AC[o,A),并f(0)＝f(h)＝0.则有integral from n=0 to h(|f(x)f(x)|dx)≤h/4 integral from n=0 to h(|f'(x)|~2dx)这个不等式叫做Opial不等式.许多数学家对它曾进行过研究.在此我们给予有意义的改进:integral from n=0 to h (|ff'|dx)≤1/2(h/2)^(2/Q)(integral from n=0 to h(|f'|~pdx))^((2/p)-(2/Q)){(integral from n=0 to h(|f'|~pdx))~2-1/4(integral from n=0 to h(|f'|~pcos(2πx/h)dx)~2)}((?)/Q)其中I<P≤2,Q＝p/(P—1)．(2)显然比(1)优秀,实际上我们已证得更一般的结果.展开更多
In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new esti...In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.展开更多
文摘设:f(x)∈AC[o,A),并f(0)＝f(h)＝0.则有integral from n=0 to h(|f(x)f(x)|dx)≤h/4 integral from n=0 to h(|f'(x)|~2dx)这个不等式叫做Opial不等式.许多数学家对它曾进行过研究.在此我们给予有意义的改进:integral from n=0 to h (|ff'|dx)≤1/2(h/2)^(2/Q)(integral from n=0 to h(|f'|~pdx))^((2/p)-(2/Q)){(integral from n=0 to h(|f'|~pdx))~2-1/4(integral from n=0 to h(|f'|~pcos(2πx/h)dx)~2)}((?)/Q)其中I<P≤2,Q＝p/(P—1)．(2)显然比(1)优秀,实际上我们已证得更一般的结果.
文摘In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.
