• East Asian mathematical journal
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• 제17권2호
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.159-180
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• 2013

We establish a common fixed point theorem for mappings under ${\phi}$-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

• 호남수학학술지
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• 제43권2호
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• pp.305-323
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• 2021

In the present paper, utilizing (𝜙, 𝜓)-weak contractive conditions, unique fixed point and some coincidence point results have been studied in the context of cone 2- metric spaces. Also, our obtained results generalize some results from cone metric space to cone 2-metric space. For the authenticity of the presented work, a non trivial example is also provided.

• 대한수학회논문집
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• 제25권1호
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• pp.69-82
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• 2010

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an asymptotically k-strict pseudo-contractive mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results are more general than the known results which are given by many authors. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

• 대한수학회보
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• 제50권3호
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• pp.993-1005
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• 2013

In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.

• 대한수학회지
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• 제40권1호
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• pp.29-40
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• 2003

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.

• 대한수학회보
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• 제45권3호
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• pp.573-585
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• 2008

A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.

• 한국수학교육학회지시리즈A:수학교육
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• 제21권3호
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• pp.37-39
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• 1983

• 대한수학회보
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• 제45권3호
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• pp.467-475
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• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• East Asian mathematical journal
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• 제39권1호
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• pp.1-10
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• 2023

In this paper, we introduce two kinds of implicit conditions and establish some fixed point theorems in cone S-metric spaces, which generalize the several existing results.