Advances in Mathematical Inequalities and Applications

This book is a collection of original research and survey articles on mathematical inequalities and their numerous applications in diverse areas of mathematics and engineering. It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, functionals, integrals and their applications in various branches of mathematics and related sciences; fractional integral inequalities; and weighted type integral inequalities. It also presents their wide applications in biomathematics, boundary value problems, mechanics, queuing models, scattering, and geomechanics in a concise, but easily understandable way that makes the further ramifications and future directions clear. The broad scope and high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers. All the contributing authors are leading international academics, scientists, researchers and scholars.

Auteur

PRAVEEN AGARWAL is a professor at the Department of Mathematics, Anand International College of Engineering, Jaipur, India. He has published over 130 articles on special functions and fractional calculus in several leading mathematics journals, such as Applied Mathematics and Computation, the Journal of Nonlinear Science and Applications, and the Journal of Inequalities and Applications. Recently, his research has focused on partial differential equations and fractional differential equations. He has been on the editorial boards of a number of journals, including the Maejo International Journal of Science and Technology. He has been involved in various conferences and has also been awarded numerous international research grants, such as the Research in Group by the International Centre for Mathematical Sciences and the World Academy of Sciences Visiting Scientist fellowship.

SEVER SILVESTRU DRAGOMIR is chair and professor of the theory of Inequalities at the School of Engineering and Science, Victoria University, Australia. He is an active member of the Australian Mathematical Society, the Mathematical Society of Romania, Research Group in Mathematical Inequalities and Applications, and the Working Group on Generalized Convexity. His research areas include classical mathematical analysis, convex functions, best approximation, numerical integration, geometry of Banach spaces, operator theory, variational methods, Volterra integral equations, qualitative theory of differential equations, theory and coding, guessing theory, adaptive quadrature rules, adaptive cubature rules, numerical methods for differential equations, numerical methods for PDEs, game theory and Kolmogorov complexity.

MOHAMED JLELI is a full professor of mathematics at King Saud University, Saudi Arabia. He obtained his PhD degree in pure mathematics entitled Constant mean curvature hypersurfaces from the Faculty of Sciences of Paris 12, France, in 2004. He has written several papers on differential geometry, partial differential equations, evolution equations, fractional differential equations and fixed point theory. He is on the editorial board of various international journals and acts as a referee for a number of international journals in mathematics.

BESSEM SAMET is a full professor of applied mathematics at King Saud University, Saudi Arabia. He obtained his PhD degree in applied mathematics entitled Topological derivative method for Maxwell equations and its applications from Paul Sabatier University, France, in 2004. His research interests include various branches of nonlinear analysis, such as fixed-point theory, partial differential equations, differential equations, and fractional calculus. He is the author/coauthor of more than 100 papers published in ISI journals. He was included in the Thomson Reuters list of Highly Cited Researchers for 2015 and 2016.

Contenu
Chapter 1. Inequalities for the Generalized k-g-Fractional Integrals in Terms of Double Integral Means.- Chapter 2. Fixed Point Approach to Solution Existence of Differential Equations.- Chapter 3. Lyapunov Inequalities for Some Differential Equations with Integral Type Boundary Conditions.- Chapter 4. A New Class of Generalized Convex Functions and Integral Inequalities.- Chapter 5. Redheffer Type Inequalities for the Fox-Wright Functions.- Chapter 6. Relations of the Extended Voigt Function with other Families of Polynomials and Numbers.- Chapter 7. Nonlinear Dynamical Model for DNA.- Chapter 8. A Variety of Nonlinear retarded Integral Inequalities of Gronwall-type and their Applications.- Chapter 9. On the Integral Inequalities for RiemannLiouville and Conformable Fractional Integrals.- Chapter 10. Weighted Integral Inequalities in Terms of OmegaFractional Integro-Differentiation.- Chapter 11. On Sherman Method to Deriving Inequalities for Some Classes of Functions Related to Convexity.- Chapter 12. Divisibility of Class Numbers of Quadratic Fields: Qualitative Aspect.- Chapter 13. Some Identities on Derangement and Degenerate Derangement Polynomials.- Chapter 14. Some Perturbed Ostrowski Type Inequalities for Twice Differentiable Functions.- Chapter 15. Comprehensive Inequalities and Equations Specified by the MittagLeffler Functions and Fractional Calculus in the Complex Plane.- Chapter 16. Novel Results on HermiteHadamard Kind Inequalities for Convex Functions by Means of (k; r)-Fractional Integral Operators.- Chapter 17. A Family of Integral Inequalities on the Interval [1; 1].- Chapter 18. A Generalization of CauchyBunyakovsky Integral Inequality via Means with Max and Min Values.