A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation.

This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space.

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory.

The first elementary exposition of core ideas of complexity theory for convex optimization, this book explores optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. Also covers polynomial-time interior-point methods.

Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type convergence of GBS operators.