• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.915-932
• /
• 2017

In this paper, we introduce a new type of additive functional equations and establish the generalized Ulam-Hyers stability for it in intuitionistic fuzzy normed space by using direct and fixed point methods.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.1
• /
• pp.1-14
• /
• 2019

We prove the generalized Hyers-Ulam-Rassias stability problem of the quadratic functional equation with involution in the fuzzy quasi ${\beta}$-normed space by using the fixed point method.

• The Pure and Applied Mathematics
• /
• v.23 no.3
• /
• pp.287-307
• /
• 2016

Using the fixed point method, we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in matrix fuzzy normed spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.1
• /
• pp.97-103
• /
• 2012

In this paper, we introduce the notion of the statist-cally fuzzy convergent sequence and the statistical fuzzy ${\alpha}$-Cauchy sequence of fuzzy points in a fuzzy normed linear space. And investigate some related properties.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.1
• /
• pp.143-147
• /
• 2007

With a new ordinary norm as an analogy of Krishna and Sarma[5] and Bag and Samanta[1], we will characterize the notions of the convergence of the sequences of fuzzy points, the fuzzy, ${\alpha}$-Cauchy sequence and fuzzy completeness.

• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.349-361
• /
• 2023

In this article, we construct lacunary ∆^m-statistical convergence for triple sequences within the context of intuitionistic fuzzy n-normed spaces (IFnNS). For lacunary ∆^m-statistical convergence of triple sequence in IFnNS, we demonstrate numerous results. For this innovative notion of convergence, we further built lacunary ∆^m-statistical Cauchy sequences and offered the Cauchy convergence criterion.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.5
• /
• pp.639-642
• /
• 2005

In this paper, we introduce the notions of the convergence in the sense of ${\alpha}$-level and the fuzzy completeness on a fuzzy normed linear space. And we investigate related properties.

• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.237-251
• /
• 2011

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We dene the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.1
• /
• pp.29-46
• /
• 2019

We introduce a generalized cubic functional equation and investigate the Hyers-Ulam stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-fuzzy anti-${\beta}$-Banach space by both the direct method and the fixed point method.

• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.93-104
• /
• 2024

In this paper, we will prove a fixed point theorem for self-mappings on a generalized quasi-ordered metric space which is a generalization of the concept of a generalized metric space with a partial order and we investigate a genralized quasi-ordered metric space related with fuzzy normed spaces. Further, we prove the stability of some functional equations in fuzzy normed spaces as an application of our fixed point theorem.