• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.2
• /
• pp.197-206
• /
• 2006

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.311-319
• /
• 2015

In this article, we consider a modified quadratic functional equation and then investigate its generalized Hyers-Ulam stability theorem in quasi-${\beta}$-normed spaces.

• The Pure and Applied Mathematics
• /
• v.20 no.1
• /
• pp.51-57
• /
• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• Korean Journal of Mathematics
• /
• v.27 no.1
• /
• pp.81-92
• /
• 2019

We introduce a reciprocal-negative Fermat's equation generalized with constants coefficients and investigate its stability in a quasi-${\beta}$-normed space.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.2061-2070
• /
• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.18 no.2
• /
• pp.215-222
• /
• 2005

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated.

• Korean Journal of Mathematics
• /
• v.7 no.2
• /
• pp.207-213
• /
• 1999

In this paper we estimate a lower bound of the Banach-Mazur distance between a finite dimensional nonlocally convex space and its Banach envelope space by investigating the properties of the nonlocally convex space and the projection constant which are obtained by factoring the identity operator through $l^k_{\infty}$ on the quasi-normed spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1363-1371
• /
• 2016

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1511-1525
• /
• 2014

In this paper, we prove the generalized Hyers-Ulam stability results controlled by considering approximately mappings satisfying conditions much weaker than Hyers and Rassias conditions for radical quadratic and radical quartic functional equations in quasi-${\beta}$-normed spaces.

• 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.