• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.61-73
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• 2016

In this paper, we consider the problems of convergence of parallel iterative algorithms for a system of nonlinear variational inequalities and nonexpansive mappings. Strong convergence theorems are established in the frame work of real Banach spaces.

• East Asian mathematical journal
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• v.24 no.4
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• pp.339-345
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• 2008

Some equivalence conditions for the convergence of iterative sequences for set-valued contraction mapping in Banach spaces are obtained.

• East Asian mathematical journal
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• v.25 no.1
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• pp.27-37
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• 2009

In this paper, we introduce an iterative method for a pair of nonexpansive mappings. Strong convergence theorems are established in a real uniformly smooth Banach space.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.1007-1020
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• 2013

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.37-51
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• 2002

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z $\in$ C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowz$_{t}$$\in$C, t$\in$[0, 1) defined by the equation z$_{t}$ = tT(z$_{t}$)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.571-581
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• 2010

Some convergence theorems for approximating to a common fixed point of an infinite family of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in the setting of Banach spaces by using a new composite implicit iterative process with errors. The results presented in the paper generalize and improve the main results of Bai and Kim [1], Gu [4], Osilike [5], Su and Li [7], and Xu and Ori [8].

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.273-286
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• 2011

Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equations $${cf\left({\displaystyle\sum_{i=1}^n\;xi}\right)+{\displaystyle\sum_{i=2}^nf}{\left(\displaystyle\sum_{i=1}^n\;x_i-(n+c-1)x_j\right)}\\ {=(n+c-1)\;\left(f(x_1)+c{\displaystyle\sum_{i=2}^n\;f(x_i)}+{\displaystyle\sum_{i in fuzzy Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.465-473
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• 2003

Introducing the concept of a sequentially condensing operator in a more general framework, we give a new fixed point theorem for sequentially condensing operators in Banach spaces, with the aid of attractors.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.151-161
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• 2008

We prove that a countably condensing operator defined on a closed wedge in a Banach space has a fixed point if it is strictly quasibounded, by using an index theory for such operators. From this, the existence of eigenvalues and surjectivity are deduced.