AbstractUsing the mathematical induction and Cauchy's mean-value theorem, for any positive number r, we prove that n+kn+m+k<1n∑n+ki=k+1ir/1n+m∑n+m+ki=k+1ir1/r, where n and m are natural numbers, k is a nonnegative integer. The lower bound is best possible. This inequality generalizes the Alzer's inequality [J. Math. Anal. Appl.179 (1993), 396–402]. An open problem is proposed
AbstractWe prove that the inequality∑k=1nxkyk2≤∑k=1nyk∑k=1nα+βkx2kyk∗holds for all natural numbersna...
AbstractWe prove the following results: (i) Let p⩾1 be a real number and let n⩾2 be an integer. If (...
By using a method of [5] we obtain a simpler proof of a result of Chao-Ping Chen and Feng Qi [2]. B...
AbstractLet {an}n=1∞ be a strictly increasing positive sequence, and let m be a natural number and r...
AbstractUsing the mathematical induction and Cauchy's mean-value theorem, for any positive number r,...
Abstract. Let {an}∞n=1 be an increasing sequence of positive real numbers. Under certain conditions ...
n=1 be a positive, strictly increasing, and logarithmically concave sequence satisfying (an+1/an) n ...
Discussing a series of inequalities, B. Bollobás reminds us in [3] that Harald Bohr wrote: “All ana...
AbstractA generalization of Alzer's inequality is proved. It is shown that this inequality is satisf...
AbstractIn this article, using the properties of the power mean, the author proves the inequalityna1...
Abstract. Let f be a strictly increasing convex (or concave) functions on (0, 1], then, for k being ...
Abstract. If the sequence {ai} i=1 satisfies △ai = ai+1 − ai> 0, △ 2ai = △(△ai) = ai+2 − 2ai+1 +...
AbstractThis note gives a short alternative proof of one of the inequalities in an article by H. Alz...
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only indu...
In this article, using binomial series, we get some interesting recursive identities concerning AGM...
AbstractWe prove that the inequality∑k=1nxkyk2≤∑k=1nyk∑k=1nα+βkx2kyk∗holds for all natural numbersna...
AbstractWe prove the following results: (i) Let p⩾1 be a real number and let n⩾2 be an integer. If (...
By using a method of [5] we obtain a simpler proof of a result of Chao-Ping Chen and Feng Qi [2]. B...
AbstractLet {an}n=1∞ be a strictly increasing positive sequence, and let m be a natural number and r...
AbstractUsing the mathematical induction and Cauchy's mean-value theorem, for any positive number r,...
Abstract. Let {an}∞n=1 be an increasing sequence of positive real numbers. Under certain conditions ...
n=1 be a positive, strictly increasing, and logarithmically concave sequence satisfying (an+1/an) n ...
Discussing a series of inequalities, B. Bollobás reminds us in [3] that Harald Bohr wrote: “All ana...
AbstractA generalization of Alzer's inequality is proved. It is shown that this inequality is satisf...
AbstractIn this article, using the properties of the power mean, the author proves the inequalityna1...
Abstract. Let f be a strictly increasing convex (or concave) functions on (0, 1], then, for k being ...
Abstract. If the sequence {ai} i=1 satisfies △ai = ai+1 − ai> 0, △ 2ai = △(△ai) = ai+2 − 2ai+1 +...
AbstractThis note gives a short alternative proof of one of the inequalities in an article by H. Alz...
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only indu...
In this article, using binomial series, we get some interesting recursive identities concerning AGM...
AbstractWe prove that the inequality∑k=1nxkyk2≤∑k=1nyk∑k=1nα+βkx2kyk∗holds for all natural numbersna...
AbstractWe prove the following results: (i) Let p⩾1 be a real number and let n⩾2 be an integer. If (...
By using a method of [5] we obtain a simpler proof of a result of Chao-Ping Chen and Feng Qi [2]. B...
DOI
Add to ORKG