This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Harmonic Hermite-Hadamard inequalities involving Mittag-Leffler function
(Aslam Noor).- Two dimensional Trapezium inequalities via pq-convex
functions (Aslam Noor).- New k-conformable fractional integral inequalities
(Uzair Awan).- On The Hyers-Ulam-Rassias Approximately Ternary Cubic Higher
Derivations (Kenary).- Hyers-Ulam stability for differential equations and
partial differential equations via Gronwall Lemma (Mariana).- On b-metric
spaces and Brower and Schauder fixed point principles
(Czerwik).- Deterministic Prediction Theory (Daras).- Accurate Approximations
of the weighted exponential Beta function (Sever Dragomir).- On the
multiplicity of the zeros of polynomials with constrained coefficients
(Erdelyi).- Generalized barycentric coordinates and sharp strongly negative
definite multidimensional numerical integration (Guessab).- Further results
on continuous random variables via fractional integrals (Agarwal).- Nonunique
fixed points on partial metric spaces via control functions
(Karapnar).- Some new refinement of Gauss-Jacobi and Hermite-Hadamard type
integral inequalities (Kashuri).- New trapezium type inequalities for
preinvex functions via generalized fractional integral operators and their
applications (Kashuri).- New Trapezoid Type Inequalities for Generalized
Exponentially Strongly Convex Functions (Jichang).- Additive-quadratic
-functional equations in -homogeneous normed spaces (Park).- Stability of
bi-additive s-functional inequalities and quasi-multipliers (Park).- On the
stability of some functional equations and s-functional inequalities
(Najati).- Stability of the Cosine-Sine functional equation on amenable
groups (Elhoucien).- Introduction to Halanay lemma, via weakly Picard
operator theory (Petrusel).- An inequality related to Möbius transformations
(Suksumran).- On a Half-Discrete Hilbert-Type Inequality in the Whole Plane
with the Hyperbolic Tangent Function and Parameters (Rassias).- Analysis of
Apostol-type numbers and polynomials with their approximations and asymptotic
behavior (Simsek).- A general lower bound for the asymptotic convergence
factor (Tsirivas).- Inequalities for mean dual affine quermassintegrals
(Cheung).- A Reduced-Basis Polynomial-Chaos Approach with a Multi-Parametric
Truncation Scheme for Problems with Uncertainties (Zygiridis).
Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 46.
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