By Panos M. Pardalos, Themistocles M. Rassias
The contributions during this quantity target to deepen knowing of a few of the present study difficulties and theories in sleek issues reminiscent of calculus of adaptations, optimization thought, advanced research, actual research, differential equations, and geometry. functions to those components of arithmetic are awarded in the large spectrum of study in Engineering technological know-how with specific emphasis on equilibrium difficulties, complexity in numerical optimization, dynamical platforms, non-smooth optimization, advanced community research, statistical versions and knowledge mining, and effort structures. extra emphasis is given to interdisciplinary learn, even if matters are taken care of in a unified and self-contained demeanour. The presentation of tools, idea and purposes makes this tribute a useful reference for lecturers, researchers, and different execs attracted to natural and utilized study, philosophy of arithmetic, and arithmetic schooling. a few evaluation papers released during this quantity could be quite necessary for a broader viewers of readers in addition to for graduate scholars who look for the newest details.
Constantin Carathéodory’s wide-ranging effect within the overseas mathematical group used to be visible in the course of the first Fields Medals awards on the overseas Congress of Mathematicians, Oslo, 1936. medals have been offered, one to Lars V. Ahlfors and one to Jesse Douglass. It was once Carathéodory who provided either their works throughout the establishing of the foreign Congress. This quantity comprises major papers in technology and Engineering devoted to the reminiscence of Constantin Carathéodory and the spirit of his mathematical effect.
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Extra info for Contributions in Mathematics and Engineering: In Honor of Constantin Carathéodory
Appl. 307, 370–386 (2005) 7. : Some new refined Hardy type inequalities with general kernels via superquadratic and subquadratic functions. Aequationes Math. 79(1), 157–172 (2010) (On line March 2010) 8. : Some new scales of refined Hardy type inequalities. Math. Inequal. Appl. 17, 1105–1114 (2014) 9. : On -quasiconvexity, superquadracity and twosided reversed Jensen type inequalities. Math. Inequal. Appl. 18(2), 615–628 (2015) 10. : Exponential convexity, positive semi-definite matrices and fundamental inequalities.
17, 1105–1114 (2014) 9. : On -quasiconvexity, superquadracity and twosided reversed Jensen type inequalities. Math. Inequal. Appl. 18(2), 615–628 (2015) 10. : Exponential convexity, positive semi-definite matrices and fundamental inequalities. J. Math. Inequal. 4(2), 171–189 (2010) 11. : Functional inequalities for superquadratic functions. Int. J. Pure Appl. Math. 43(4), 5037–549 (2008) 12. : Superquadratic functions and refinements of some classical inequalities. J. Korean Math. Soc. 45, 513–525 (2008) 13.
Lemma 3 (Montgomery Identity). Let a; b; s; t 2 R with 0 Ä a < b, and let f W Œa; b ! 0; 1. t; s/ WD s˛ a˛ ˛ s˛ b˛ ˛ W a Ä s < t; (14) W t Ä s Ä b: Proof. s/d˛ s: t t u Adding and solving for f yields the result. Theorem 8 (Ostrowski Inequality). Let a; b; s; t 2 R with 0 Ä a < b, and let f W Œa; b ! 0; 1. a;b/ This inequality is sharp in the sense that the right-hand side of (15) cannot be replaced by a smaller one. Proof. s/d s ˛ ˛ ˇ b a˛ a ˇ ˇ Ã ÂZ t ˇ ˛ Z bˇ ˛ ˇs ˇs a˛ ˇˇ b˛ ˇˇ M˛ ˇ ˇ Ä ˛ s C s d d ˇ ˛ ˇ ˛ ˇ ˛ ˇ ˛ b a˛ a t Ã ÂZ t Â ˛ Ã Ã Z bÂ ˛ s b a˛ s˛ M˛ D ˛ d˛ s C d˛ s ˛ b a ˛ ˛ a t Â ˛ Ã Â Ã2 !
Contributions in Mathematics and Engineering: In Honor of Constantin Carathéodory by Panos M. Pardalos, Themistocles M. Rassias