Themistocles M. Rassias

Stability of Functional Equations in Several Variables

Approximately additive and approximately linear mappings stability of the quadratic functional equation generalizations - the method of invariant means approximately multiplicative mappings - superstability stability of functional equations for trigonometric and similar functions functions with bounded nth differences approximately convex functions stability of the generalized orthogonality functional equation stability and set-valued mappings stability of stationary and minimum points functional congruences quasi-additive functions and related topics.

On the Stability of Functional Equations and a Problem of Ulam

In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory.

Some aspects of variational inequalities

Abstract In this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence, uniqueness, computational properties, various generalizations, sensitivity analysis and their applications. We also propose some open problems with sufficient information and references, so that someone may attempt solution(s) in his/her area of special interest. We also include some new results, which we have recently obtained.

Topics in polynomials : extremal problems, inequalities, zeros

General concept of polynomials elementary inequalities zeros of polynomials special classes of polynomials extremal problems for polynomials inequalities connected with trigonometric sums.

Stability of ψ-additive mappings: applications to nonlinear analysis

The Hyers-Ulam stability of mappings is in development and several authors have remarked interesting applications of this theory to various mathematical problems. In this paper some applications in nonlinear analysis are presented, especially in fixed point theory. These kinds of applications seem not to have ever been remarked before by other authors.

Topics in Nonlinear Analysis and Applications

Stability of functional equations isometric mappings cones and complementarity problems metrics on cones zero-epi mappings variational principles maximal element principles.

Ostrowski type inequalities and applications in numerical integration

List of Figures. List of Tables. Preface. List of Symbols. 1. Generalizations of the Ostrowski Inequality and Applications S.S. Dragomir, T.M. Rassias. 2. Integral Inequalities for eta-Times Differentiable Mappings A. Sofo. 3. Three Point Quadrature Rules P. Cerone, S.S. Dragomir. 4. Product Branched Peano Kernels and Numerical Integration P. Cerone. 5. Ostrowski Type Inequalities for Multiple Integrals N.S. Barnett, et al. 6. Results for Double Integrals Based on an Ostrowski Type Inequality G. Hanna. 7. Product Inequalities and Weighted Quadrature J. Roumeliotis. 8. Some Inequalities for the Riemann-Stieltjes Integral S.S. Dragomir, T.M. Rassias. Index.

On the asymptoticity aspect of Hyers-Ulam stability of mappings

The object of the present paper is to prove an asymptotic analogue of Th. M. Rassias’ theorem obtained in 1978 for the Hyers-Ulam stability of mappings.

Functional equations and inequalities

Preface. On the Stability of a Functional Equation for Generalized Trigonometric Functions R. Badora. Some Notes on Two-Scale Difference Equations L. Berg, G. Plonka. Some Demand Functions in a Duopoly Market with Advertising E. Castillo, et al. Solutions of a Functional Inequality in a Special Class of Functions M. Czerni. On Dependence of Lipschitzian Solutions of Nonlinear Functional Inequality on an Arbitrary Function M. Czerni. The Problem of Expressibility in Some Extensions of Free Groups V. Faiziev. On a Pythagorean Functional Equation Involving Certain Number Fields J.L. Garcia-Roig, J. Salillas. On a Conditional Cauchy Functional Equation Involving Cubes J.L. Garcia-Roig, E. Martin-Gutierrez. Hyers-Ulam Stability of Hosszus Equation P. Gavruta. The Functional Equation of the Square Root Spiral K.J. Heuvers, et al. On the Superstability of the Functional Equation f(xy)=f(x)y S.-M. Jung. Replicativity and Function Spaces H.-H. Kairies. Normal Distributions and the Functional Equation f(x+y) g(x-y) = f(x) f(y) g(x) g(-y) P.L. Kannappan. On the Polynomial-Like Iterative Functional Equation J. Matkowski, W. Zhang. Distribution of Zeros and Inequalities for Zeros of Algebraic Polynomials G.V. Milovanovic, T.M. Rassias. A Functional Definition of Trigonometric Functions N.N. Neamtu. A Qualitative Study of Lobachevksys Complex Functional Equation N.N. Neamtu. Smooth Solutions of an Iterative Functional Equation J.-G. Si, et al. Set-Valued Quasiconvex Functions and their Constant Selections W. Smajdor. Entire Solution of the Hille-type Functional Equation A. Smajdor, W. Smajdor. Ulams Problem, Hyers Solution - and to Where they Led L. Szekelyhidi. ASeparation Lemma for the Construction of Finite Sums Decompositions W. Tutschke. Aleksandrov Problem and Mappings which Preserve Distances S. Xiang. On Some Subclasses of Harmonic Functions S. Yalcin, et al. Index.

Some classes of infinite series associated with the Riemann Zeta and Polygamma functions and generalized harmonic numbers

The authors aim at presenting a systematic investigation of several families of infinite series which are associated with the Riemann Zeta function, the Digamma (and Polygamma) functions, the harmonic (and generalized harmonic) numbers, and the Stirling numbers of the first kind. Relevant connections of the results derived here with those considered in many earlier works on this subject are also indicated.