• East Asian mathematical journal
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• v.6 no.1
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• pp.45-62
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• 1990

• Bulletin of the Korean Mathematical Society
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• v.11 no.1
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• pp.11-13
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• 1974

• Kyungpook Mathematical Journal
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• v.26 no.2
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• pp.187-215
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• 1986

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.783-796
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• 2010

We introduce a new iterative algorithm for equilibrium and fixed point problems of three hemi-relatively nonexpansive mappings by the CQ hybrid method in Banach spaces, Our results improve and extend the corresponding results announced by Xiaolong Qin, Yeol Je Cho, Shin Min Kang [Xiaolong Qin, Yeol Je Cho, Shin Min Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225 (2009) 20-30], P. Kumam, K. Wattanawitoon [P. Kumam, K. Wattanawitoon, Convergence theorems of a hybrid algorithm for equilibrium problems, Nonlinear Analysis: Hybrid Systems (2009), doi:10.1016/j.nahs.2009.02.006], W. Takahashi, K. Zembayashi [W. Takahashi, K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008) doi:10.1155/2008/528476] and others therein.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.623-646
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• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.527-529
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• 2012

It is proved that the fractional Sobolev spaces $W^s_p(\mathbb{R}^n)$ 0 < $s$ < $n$, are compactly embedded into Lebesgue spaces $L^q(\Omega)$ for some bounded set $\Omega$­.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.393-399
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• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.369-378
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• 2005

In this paper we will consider the weighted composition operator $W=uC_{\varphi}$ between two different $L^p(X,\;\Sigma,\;\mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\varphi$ that induce weighted composition operators between $L^p-spaces$ by using some properties of conditional expectation operator, pair $(u,\;\varphi)$ and the measure space $(X,\;\Sigma,\;\mu)$. Also, Fredholmness of these type operators will be investigated.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.1009-1015
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• 2010

We prove the existence of common fixed points for three self mappings satisfying contractive conditions in d-complete topological spaces. Our results are generalizations of result of Troy L. Hicks and B. E. Roades[Troy L. Hicks and B. E. Roades, Fixed points for pairs of mappings in d-complete topological spaces, Int. J. Math. and Math. Sci., 16(2)(1993), 259-266].