• 대한수학회보
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• 제34권1호
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• pp.93-102
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• 1997

Let C be a nonempty closed convex subset of a Banach space E and let $T_1, \cdots, T_N$ be nonexpansive mappings from C into itself (recall that a mapping $T : C \longrightarrow C$ is nonexpansive if $\left\$\mid$ Tx - Ty \right\$\mid$ \leq \left\$\mid$ x - y \right\$\mid$$ for all $x, y \in C$). We consider the fixed point problem for nonexpansive mappings : find a common fixed point, i.e., find a point in $\cap_{i=1}^N Fix(T_i)$, where $Fix(T_i) := {x \in C : x = T_i x}$ denotes the set of fixed points of $T_i$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권3호
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• pp.285-298
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• 2015

In [41], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed positive integer l holds for all x₁, ⋯ , x_2l ∈ V . For the above equality, we can define the following functional equation Using the fixed point method, we prove the Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

• 대한수학회논문집
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• 제31권1호
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• pp.139-145
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• 2016

In this paper, some new fixed point theorems for condensing mappings are established based on a well known result of Petryshyn. We use several Leray-Schauder type conditions to prove new fixed point results. We also obtain generalizations of Altman's theorem and Petryshyn's theorem as well.

• 대한수학회논문집
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• 제24권4호
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• pp.565-579
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• 2009

In this paper, we give some new fixed point theorems for contractive type mappings in intuitionistic fuzzy metric spaces. We improve and generalize the well-known fixed point theorems of Banach [4] and Edelstein [8] in intuitionistic fuzzy metric spaces. Our main results are intuitionistic fuzzy version of Fang's results [10]. Further, we obtain some applications to validate our main results to product spaces.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.311-335
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• 2023

Fixed point theory is the center of focus for many mathematicians from last few decades. A lot of generalizations of the Banach contraction principle have been established. In this paper, we introduce the concepts of 𝜃-contraction and 𝜃-𝜑-contraction in quasi-metric spaces to study the existence of the fixed point for them.

• East Asian mathematical journal
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• 제27권1호
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.73-82
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• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.451-474
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• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.667-674
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• 2009

In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.

• 충청수학회지
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• 제29권3호
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• pp.453-464
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• 2016

In this paper, we investigate the solution of the following functional inequality $$N(f(x)+f(y)+f(z),t){\geq}N(f(x+y+z),mt)$$ for some fixed real number m with $\frac{1}{3}$ < m ${\leq}$ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.