• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.261-269
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• 2014

In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation $$(k+1)f(x+y)+f(x+{\sigma}(y))+kf({\sigma}(x)+y)-2(k+1)f(x)-2(k+1)f(y)=0$$ with an involution ${\sigma}$ for a fixed non-zero real number k with $k{\neq}-1$.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.339-348
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• 2014

In this paper, we investigate the solution of the following functional inequality $${\parallel}f(x)+f(y)+f(az),\;w{\parallel}{\leq}{\parallel}f(x+y)-f(-az),\;w{\parallel}$$ for some xed non-zero integer a, and prove the generalized Hyers-Ulam stability of it in non-Archimedean 2-normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.757-770
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• 2009

In this paper, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation (0.1) f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f(-2y) - 4f(y) - 4f(-y) in Banach spaces.

• East Asian mathematical journal
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• v.31 no.5
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• pp.627-634
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• 2015

In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

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

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.67-83
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• 2009

Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.729-743
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• 2016

In the current work, the intuitionistic fuzzy version of Hyers-Ulam stability for a nonic functional equation by applying a fixed point method is investigated. This way shows that some fixed points of a suitable operator can be a nonic mapping.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2008.05a
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• pp.184-189
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• 2008

The change in a society have brought about other changes in the overall areas of culture and art. And have brought the advent of "object", which is a unique cultural aspect. The object became a trend of the world in a culture and art. This trend has satisfied the modern people who have look for new visual stimulation. The object appears well in the spaces restaurants and bars where are reflected in consumer's needs and change of life pattern. The reason is that the spaces restaurants and bars have expressed the differentiated and individualized image with the characteristic of the times. There are three types of the expressed characteristics of objects in interior design. These are visual, functional, and emotional characteristics. But in this study it could not be found that it characterized with one concrete vocabulary and concept. Therefore, it is need to understand the various tendency which expressed characteristics of objects in the spaces restaurants and bars.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.117-135
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• 2021

Our purpose in this paper is to introduce the concept of complex valued convex metric spaces and introduce an analogue of the Picard-Ishikawa hybrid iterative scheme, recently proposed by Okeke [24] in this new setting. We approximate (common) fixed points of certain contractive conditions through these two new concepts and obtain several corollaries. We prove that the Picard-Ishikawa hybrid iterative scheme [24] converges faster than all of Mann, Ishikawa and Noor [23] iterative schemes in complex valued convex metric spaces. Also, we give some numerical examples to validate our results.