Generalizations of Hardy's integral inequalities.
Yang, Bicheng, Debnath, Lokenath (1999)
International Journal of Mathematics and Mathematical Sciences
Cheung, Wing-Sum (2001)
International Journal of Mathematics and Mathematical Sciences
Shoshana Abramovich, Slavica Ivelić, Josip Pečarić (2010)
Open Mathematics
We present integral versions of some recently proved results which improve the Jensen-Steffensen and related inequalities for superquadratic functions. For superquadratic functions which are not convex we get inequalities analogous to the integral Jensen-Steffensen inequality for convex functions. Therefore, we get refinements of all the results which use only the convexity of these functions. One of the inequalities that we obtain for a superquadratic function φ is , where and which under...
Civljak, A., Dedic, Lj. (2010)
Banach Journal of Mathematical Analysis [electronic only]
Pan, Wenhai, Zhu, Ling (2009)
Journal of Inequalities and Applications [electronic only]
Liu, Zheng (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
D. M. Bǎtineţu-Giurgiu, Neculai Stanciu (2013)
The Teaching of Mathematics
Milica Bakula, Marko Matić, Josip Pečarić (2009)
Open Mathematics
We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.
Li, Ai-Jun, Wang, Xue-Min, Chen, Chao-Ping (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Kechriniotis, A.I., Assimakis, N.D. (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Matić, M., Pečarić, J., Ujević, N. (2000)
Journal of Inequalities and Applications [electronic only]
Qi, Feng (2000)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Horváth, László (2009)
Journal of Inequalities and Applications [electronic only]
Chen, Tieling, Sinnamon, Gord (2002)
Journal of Inequalities and Applications [electronic only]
Petr Gurka (1984)
Časopis pro pěstování matematiky
Saidi, Fathi B. (2003)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Zhu, Ling (2009)
Journal of Inequalities and Applications [electronic only]
J.K. Baksalary, S. Puntanen (1991)
Aequationes mathematicae
Agnew, Robert A., Pecaric, Josip E. (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Robert Černý (2013)
Applications of Mathematics
Let , , be a bounded connected domain of the class for some . Applying the generalized Moser-Trudinger inequality without boundary condition, the Mountain Pass Theorem and the Ekeland Variational Principle, we prove the existence and multiplicity of nontrivial weak solutions to the problem where is a Young function such that the space is embedded into exponential or multiple exponential Orlicz space, the nonlinearity has the corresponding critical growth, is a continuous potential,...