Comparison theorems for summability methods of sequences of fuzzy numbers

In this study we compare Ces\`{a}ro and Euler weighted mean methods of summability of sequences of fuzzy numbers with Abel and Borel power series methods of summability of sequences of fuzzy numbers. Also some results dealing with series of fuzzy numbers are obtained.Comment: publication information is added, typos correcte

Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers

We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results

On the resummation of series of fuzzy numbers via generalized Dirichlet and generalized factorial series

We introduce semicontinuous summation methods for series of fuzzy numbers and give Tauberian conditions under which summation of a series of fuzzy numbers via generalized Dirichlet series and via generalized factorial series implies its convergence. Besides, we define the concept of level Fourier series of fuzzy valued functions and obtain results concerning the summation of level Fourier series.Comment: publication information is adde

Some Tauberian Remainder Theorems for Holder Summability

In this paper, we prove some Tauberian remainder theorems that generalize the results given by Meronen and Tammeraid [Math. Model. Anal., 18(1):97– 102, 2013] for Holder summability method using the notion of the general control modulo of the oscillatory behaviour of nonnegative integer order

On the Zweier Sequence Spaces of Fuzzy Numbers

It was given a prototype constructing a new sequence space of fuzzy numbers by means of the matrix domain of a particular limitation method. That is we have constructed the Zweier sequence spaces of fuzzy numbers [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη consisting of all sequences u=(uk) such that Zηu in the spaces ℓ∞(F), c(F), and c0(F), respectively. Also, we prove that [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη are linearly isomorphic to the spaces ℓ∞(F), c(F), and c0(F), respectively. Additionally, the α(r)-, β(r)-, and γ(r)-duals of the spaces [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη have been computed. Furthermore, two theorems concerning matrix map have been given

On I-acceleration convergence of sequences of fuzzy real numbers

In this article we introduce the notion of ideal acceleration convergence of sequences of fuzzy real numbers. We have proved a decomposition theorem for ideal acceleration convergence of sequences as well as for subsequence transformations and studied different types of acceleration convergence of fuzzy real valued sequence

Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics