Ravi P. Agarwal

Bio: Ravi P. Agarwal is an academic researcher from Texas A&M University. The author has contributed to research in topics: Boundary value problem & Nonlinear system. The author has an hindex of 79, co-authored 1595 publications receiving 34854 citations. Previous affiliations of Ravi P. Agarwal include Bohai University & King Fahd University of Petroleum and Minerals.

Applications of q-Calculus in Operator Theory

Abstract: Introduction of q-calculus.- q-Discrete operators and their results.- q-Integral operators.- q-Bernstein type integral operators.- q-Summation-integral operators.- Statistical convergence of q-operators.- q-Complex operators.

Fixed Point Theory for Lipschitzian-type Mappings with Applications

Abstract: Fundamentals.- Convexity, Smoothness, and Duality Mappings.- Geometric Coefficients of Banach Spaces.- Existence Theorems in Metric Spaces.- Existence Theorems in Banach Spaces.- Approximation of Fixed Points.- Strong Convergence Theorems.- Applications of Fixed Point Theorems.

Inequalities on Time Scales: A Survey

Abstract: The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger (1988), is an area of mathematics which is currently receiving considerable attention. Although the basic aim of this is to unify the study of differential and difference equations, it also extends these classical cases to cases “in between”. In this paper we present time scales versions of the inequalities: Holder, Cauchy-Schwarz, Minkowski, Jensen, Gronwall, Bernoulli, Bihari, Opial, Wirtinger, and Lyapunov. 1. Unifying Continuous and Discrete Analysis In 1988, Stefan Hilger [13] introduced the calculus on time scales which unifies continuous and discrete analysis. A time scale is a closed subset of the real numbers. We denote a time scale by the symbol T . For functions y defined on T , we introduce a so-called delta derivative y∆ . This delta derivative is equal to y (the usual derivative) if T = R is the set of all real numbers, and it is equal to ∆y (the usual forward difference) if T = Z is the set of all integers. Then we study dynamic equations f (t; y; y∆; y∆ 2 ; : : : ; y∆ n ) = 0; which may involve higher order derivatives as indicated. Along with such dynamic equations we consider initial values and boundary conditions. We remark that these dynamic equations are differential equations when T = R and difference equations when T = Z . Other kinds of equations are covered by them as well, such as q difference equations, where T = q := fqkj k 2 Zg[ f0g for some q > 1 and difference equations with constant step size, where T = hZ := fhkj k 2 Zg for some h > 0: Particularly useful for the discretization purpose are time scales of the form T = ftkj k 2 Zg where tk 2 R; tk < tk+1 for all k 2 Z: Mathematics subject classification (2000): 34A40, 39A13.

Infinite Interval Problems for Differential, Difference and Integral Equations

Abstract: Preface. 1. Second Order Boundary Value Problems. 2. Higher Order Boundary Value Problems. 3. Continuous Systems. 4. Integral Equations. 5. Discrete Systems. 6. Equations in Banach Spaces. 7. Multivalued Equations. 8. Equations on Time Scales. Subject Index.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Finite-Time Stability of Continuous Autonomous Systems

Abstract: Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.