"Functional Calculus" ed. by Kamal Shah, Baver Okutmuştur

The aim of this book is to present a broad overview of the theory and applications related to functional calculus. The book is based on two main subject areas: matrix calculus and applications of Hilbert spaces. The concept of this book covers topics that will be of interest not only for students but also for researchers and professors in this field of mathematics. The authors of each chapter convey a strong emphasis on theoretical foundations in this book.

Determinantal representations of the core inverse and its generalizations, new series formulas for matrix exponential series, results on fixed point theory, and chaotic graph operations and their fundamental group are contained under the umbrella of matrix calculus. In addition, numerical analysis of boundary value problems of fractional differential equations are also considered here. In addition, reproducing kernel Hilbert spaces, spectral theory as an application of Hilbert spaces, and an analysis of PM10 fluctuations and optimal control are all contained in the applications of Hilbert spaces.


Contents
1.Determinantal Representations of the Core Inverse and Its Generalizations
2.New Matrix Series Formulae for Matrix Exponentials and for the Solution of Linear Systems of Algebraic Equations
3.Fixed Point Theorems of a New Generalized Nonexpansive Mapping
4.Folding on the Chaotic Graph Operations and Their Fundamental Group
5.A Survey on Hilbert Spaces and Reproducing Kernels
6.Analytical Applications on Some Hilbert Spaces
7.Spectral Observations of PM10 Fluctuations in the Hilbert Space
8.Optimal Control of Evolution Differential Inclusions with Polynomial Linear Differential Operators
9.Spectral Analysis and Numerical Investigation of a Flexible Structure with Nonconservative Boundary Data
10.Integral Inequalities and Differential Equations via Fractional Calculus
11.Approximate Solutions of Some Boundary Value Problems by Using Operational Matrices of Bernstein Polynomials