• Kyungpook Mathematical Journal
• /
• 제52권4호
• /
• pp.397-404
• /
• 2012

In this article, the reverse q-H$\ddot{o}$lder type inequality and two dimensional q-H$\ddot{o}$lder's inequality are established. We also obtain some q-integral inequalities by using q-H$\ddot{o}$lder's inequality which give q-Hardy's inequalities as spacial cases.

• East Asian mathematical journal
• /
• 제32권1호
• /
• pp.27-33
• /
• 2016

Generalized $H{\ddot{o}}lder$ inequality developed by H. Qiang and Z. Hu is further refined. Also, generalized$H{\ddot{o}}lder$ inequality developed by X. Yang is further refined.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제17권2호
• /
• pp.189-197
• /
• 2010

We give an upper bound for the estimation of the difference between both sides of the well-known H$\ddot{o}$lder's inequality. Moreover, an upper bound for the estimation of the difference of the integral form of H$\ddot{o}$lder's inequality is also obtained. The results of this paper are natural generalizations and refinements of those of [2-4].

• 대한수학회보
• /
• 제50권3호
• /
• pp.901-914
• /
• 2013

Kwon and Bae gave an interpolation for a continuous form of H$\ddot{o}$lder's inequality for a real-valued bounded measurable function on a product of measure spaces. It is given some generalizations of their result.

• Journal of applied mathematics & informatics
• /
• 제37권5_6호
• /
• pp.491-506
• /
• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• East Asian mathematical journal
• /
• 제29권5호
• /
• pp.537-543
• /
• 2013

Recent results of Wu and Tian on refined H$\ddot{o}$lder's inequality for two sequences are extended to the case of three sequences.

• East Asian mathematical journal
• /
• 제23권2호
• /
• pp.229-246
• /
• 2007

Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.

• 충청수학회지
• /
• 제31권3호
• /
• pp.321-324
• /
• 2018

We present a new and simple proof of improved Carleson's inequality.

• 호남수학학술지
• /
• 제42권2호
• /
• pp.301-318
• /
• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• Kyungpook Mathematical Journal
• /
• 제46권1호
• /
• pp.19-29
• /
• 2006

In this paper, we obtain some inequalities similar to Hilbert type. Some new inequalities are also given.