Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

Abdulaziz M Alanazi,G Muhiuddin,Abdelhalim Ebaid,K Tamilvanan,Ebtehaj N Alenze,K Loganathan

doi:10.3390/math8071050

Abdulaziz M Alanazi, G Muhiuddin + Show 4 more

Open Access

https://doi.org/10.3390/math8071050

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Abstract

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.

Highlights

Introduction and PreliminariesSometimes in modeling solved problems there can be a degree of uncertainty in the limitations used within the model or a few capacities can be vague
Bag and Samanta [27], following Cheng and Mordeson [28], proposed a fuzzy norm such that the corresponding fuzzy metric is of the Kramosil and Michalek kind [29]
They set up a decomposition theorem of a fuzzy norm into a group of crisp norms and researched a few properties of fuzzy normed spaces [30]

Summary

Introduction and Preliminaries

Sometimes in modeling solved problems there can be a degree of uncertainty in the limitations used within the model or a few capacities can be vague. Bag and Samanta [27], following Cheng and Mordeson [28], proposed a fuzzy norm such that the corresponding fuzzy metric is of the Kramosil and Michalek kind [29] They set up a decomposition theorem of a fuzzy norm into a group of crisp norms and researched a few properties of fuzzy normed spaces [30]. We utilize the notions of fuzzy normed spaces given in [27,43,44] to explore a fuzzy version of the generalized Hyers–Ulam stability for the finite variable additive functional equation l. (iii ) d( x, b) ≤ 1−1 L d( x, Λx ) for all x ∈ Y

General Solution

Direct Method

Result and Discussion

Counter Example

Conclusions