We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of...
We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of the...
Statistical convergence has been explored in numerous contexts such as fuzzy logic theory. Here, the authors approach the subject by approximating a function by linear operators, focusing on situations in which the classical limit is not effective.
Statistical convergence has been explored in numerous contexts such as fuzzy logic theory. Here, the authors approach the subject by approximating a f...
Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given....
Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first f...
The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators....
The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been i...
This book solves mathematical analysis problems using popular software packages. Besides fundamental theoretical notions, the book offers many exercises solved both mathematically and by computer, using Matlab 7.9, Mathcad 14, Mathematica 8 or Maple 15.
This book solves mathematical analysis problems using popular software packages. Besides fundamental theoretical notions, the book offers many exercis...
The theory presented in this book is destined and expected to find applications to all aspects of fuzziness from theoretical to practical in almost all sciences, technology, finance and industry, as well as within pure mathematics.
The theory presented in this book is destined and expected to find applications to all aspects of fuzziness from theoretical to practical in almost al...
Real Analysis is a discipline of intensive study in many institutions of higher education, because it contains useful concepts and fundamental results in the study of mathematics and physics, of the technical disciplines and geometry. This book is the first one of its kind that solves mathematical analysis problems with all four related main software Matlab, Mathcad, Mathematica and Maple. Besides the fundamental theoretical notions, the book contains many exercises, solved both mathematically and by computer, using: Matlab 7.9, Mathcad 14, Mathematica 8 or Maple 15 programming languages. The...
Real Analysis is a discipline of intensive study in many institutions of higher education, because it contains useful concepts and fundamental results...
This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other...
This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish r...
This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex...
This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequa...
This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential...
This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are un...
