Soft Computing

, Volume 22, Issue 12, pp 3951–3957

# Tauberian theorems for weighted mean summability method of improper Riemann integrals of fuzzy-number-valued functions

Methodologies and Application

## Abstract

We consider the concept of weighted mean summability method of improper Riemann integrals of fuzzy-number-valued functions with the help of fuzzy Riemann–Stieltjes integrals introduced by Ren and Wu (Int J Theor Phys 52:2134–2151, 2013). The convergence of the improper Rieman integral implies its summability by weighted mean method, but inverse requirement is not true in general and is realized by means of supplementary conditions known as Tauberian conditions.

## Keywords

Tauberian theorems Fuzzy-number-valued function Fuzzy Riemann–Stieltjes integral Weighted mean method

## Notes

### Conflict of interest

The author declares that he has no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

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