Some new properties of generalized Hölders inequalities

Volume 9, Issue 6, pp 3638--3646 http://dx.doi.org/10.22436/jnsa.009.06.16

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Authors

Jing-Feng Tian - College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, P. R. China. Ming-Hu Ha - School of Science, Hebei University of Engineering, Handan, Hebei Province, 056038, P. R. China.

Abstract

Hölder's inequality and its various generalizations are playing very important and basic role in different branches of modern mathematics. In this paper, we give some new monotonicity properties of generalized Hölder's inequalities and then we obtain some new refinements of generalized Hölder's inequalities.

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Keywords

• Generalized Hölder's inequality
• Hölder's inequality
• monotonicity properties
• refinements.

MSC

•  26D15
•  26D10

References

• [1] O. Hölder, Über einen mittelwertsatz, Göttinger Nachr., 2 (1889), 38-47.


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• [3] F. Qi, P. Cerone, S. S. Dragomir, H. M. Srivastava, Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values , Appl. Math. Comput., 208 (2009), 129-133.


• [4] J. F. Tian, Property of a Hölder-type inequality and its application, Math. Inequal. Appl., 16 (2013), 831-841.


• [5] J. F. Tian, Properties of generalized Hölder's inequalities, J. Math. Inequal., 9 (2015), 473{480.


• [6] P. M. Vasić, J. E. Pečarić, On the Jensen inequality for monotone functions, An. Univ. Timisoara Ser. Stiint. Mat., 17 (1979), 95-104.