• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.269-283
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• 2013

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.579-591
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• 2002

New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.37-43
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• 2017

We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1839-1854
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• 2015

Brief developments in metrical fixed point theory are covered and a significant generalization of recent results obtained in [18], [27], [32] and [33] is established through an extension of the property (EA) to two sequences of self-maps using the notions of weak compatibility and implicit relation.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.201-215
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $f(x+y+z+w)\;+\;2f(x)\;+\;2f(y)\;+\;2f(z)\;+\;2f(w)\;-\;f(x+y)\;-\;f(x+z)\;-\;f(x+w)\;-\;f(y+z)\;-\;f(y+w)\;-\;f(z+w)=0$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.51-63
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(2x+y)+f(2x-y)+2f(x)-f(x+y)-f(x-y)-2f(2x)=0$$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.43-49
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• 2012

In this paper, we investigate the stability of a functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$ by using the fixed point theory in the sense of L. $C\breve{a}dariu$ and V. Radu.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.219-232
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• 2013

In this paper, we investigate the stability of the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.113-125
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• 2019

In this paper, I investigate the stability of the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.343-355
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• 2019

In this paper, we investigate the stability of the functional equation $$f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-f(ky)+{\frac{k^3+k^2-2k}{2}}f(-y)-{\frac{k^3-k^2-2k}{2}}f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.