Contributions in Mathematics and Engineering

1. Front Matter

   Pages i-xi

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2. Applications of Quasiconvexity

   • S. Abramovich

   Pages 1-23

3. Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives

   • Douglas R. Anderson

   Pages 25-43

4. Sobolev-Type Inequalities on Manifolds in the Presence of Symmetries and Applications

   • Athanase Cotsiolis, Nikos Labropoulos

   Pages 45-68

5. Generalized Minkowski Functionals

   • Stefan Czerwik, Krzysztof Król

   Pages 69-79

6. A Network Design Model Under Uncertainty

   • E. D’Amato, E. Daniele, L. Mallozzi

   Pages 81-93

7. Optimal Rational Approximation Number Sets: Application to Nonlinear Dynamics in Particle Accelerators

   • Nicholas J. Daras, Michael N. Vrahatis

   Pages 95-115

8. A Characterization Theorem for the Best L ₁ Piecewise Monotonic Data Approximation Problem

   • Ioannis C. Demetriou

   Pages 117-126

9. Supermeasures Associated to Some Classical Inequalities

   • Silvestru Sever Dragomir

   Pages 127-152

10. Remarks on Solutions of a Functional Equation Arising from an Asymmetric Switch

    • El-Sayed El-Hady, Janusz Brzdęk, Wolfgang Förg-Rob, Hamed Nassar

    Pages 153-163

11. Hyers–Ulam Stability of Wilson’s Functional Equation

    • Elhoucien Elqorachi, Youssef Manar, Themistocles M. Rassias

    Pages 165-183

12. The General Sampling Theory by Using Reproducing Kernels

    • Hiroshi Fujiwara, Saburou Saitoh

    Pages 185-204

13. Kronecker’s Products and Kronecker’s Sums of Operators

    • Michael Gil’

    Pages 205-253

14. Effective Conductivity and Critical Properties of a Hexagonal Array of Superconducting Cylinders

    • Simon Gluzman, Vladimir Mityushev, Wojciech Nawalaniec, Galina Starushenko

    Pages 255-297

15. A Survey on Durrmeyer-Type Operators

    • Vijay Gupta, Themistocles M. Rassias, Jyoti Sinha

    Pages 299-312

16. On the Imaginary Part of the Nontrivial Zeros of the Riemann Zeta Function

    • Mehdi Hassani

    Pages 313-321

17. The Ubiquitous Lambert Function and its Classes in Sciences and Engineering

    • Christina Katsimpiri, Panayotis E. Nastou, Panos M. Pardalos, Yannis C. Stamatiou

    Pages 323-342

18. A Computational Approach to the Unwrappings of the Developable Surfaces

    • Dimitrios Kodokostas

    Pages 343-351

19. Multiple Weighted Orlicz Spaces and Applications

    • Jichang Kuang

    Pages 353-375

20. Hyers–Ulam–Rassias Stability on Amenable Groups

    • Mohamed Akkouchi, Elhoucien Elqorachi, Khalil Sammad

    Pages 377-392

The contributions in this volume aim to deepen understanding of some of the current research problems and theories in modern topics such as calculus of variations, optimization theory, complex analysis, real analysis, differential equations, and geometry. Applications to these areas of mathematics are presented within the broad spectrum of research in Engineering Science with particular emphasis on equilibrium problems, complexity in numerical optimization, dynamical systems, non-smooth optimization, complex network analysis, statistical models and data mining, and energy systems. Additional emphasis is given to interdisciplinary research, although subjects are treated in a unified and self-contained manner. The presentation of methods, theory and applications makes this tribute an invaluable reference for teachers, researchers, and other professionals interested in pure and applied research, philosophy of mathematics, and mathematics education. Some review papers published in this volume will be particularly useful for a broader audience of readers as well as for graduate students who search for the latest information.    ​

Constantin Carathéodory’s wide-ranging influence in the international mathematical community was seen during the first Fields Medals awards at the International Congress of Mathematicians, Oslo, 1936. Two medals were awarded, one to Lars V. Ahlfors and one to Jesse Douglass. It was Carathéodory who presented both their works during the opening of the International Congress. This volume contains significant papers in Science and Engineering dedicated to the memory of Constantin Carathéodory and the spirit of his mathematical influence.      

• calculus of variations
• complex network analysis
• data mining
• energy systems
• optimization theory
• quasiconvexity
• superquadracity
• Jensen inequality
• Hardy inequalities
• Kolmogorov result
• Minkowski functional
• tensor product
• Hilbert spaces
• Kronecker's sum
• matrix pencil
• weighted Orlicz space
• Hyers stability
• Galois connections
• Bakhtin metric
• Ekeland variational principle

• Industrial and Systems Engineering, University of Florida, Gainesville, USA

  Panos M. Pardalos

• Department of Mathematics, National Technical Unversity of Athens Department of Mathematics, Athens, Greece

  Themistocles M. Rassias

Themistocles M. Rassias is a Professor of Mathematics at National Technical University of Athens. He holds a PhD in Mathematics from the University of California, Berkeley, and has published over fifty books and nearly three hundred journal articles.

Panos M. Pardalos serves as Distinguished Professor of Industrial and Systems Engineering at the University of Florida, as well as the Director of the Center for Applied Optimization. He holds a PhD in Computer and Information Sciences from the University of Minnesota, Minneapolis, and has published nearly twenty books and over four hundred papers. 

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