• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.407-416
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• 2023

In this paper, we introduce the concept of C^*-algebra-valued quasi b-metric space and prove some existence and uniqueness theorems. Furthermore, we prove the Hyers-Ulam stability results for fixed point problems via C^*-algebra-valued extended quasi b-metric space.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.451-461
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• 2023

In this paper, we study the fixed point property for generalized asymptotically nonexpansive mappings in the setting of p-Hadamard spaces, with p ≥ 2. We prove the strong convergence of the sequence generated by the modified two-step iterative sequence for finding a fixed point of a generalized asymptotically nonexpansive mapping in p-Hadamard spaces.

• East Asian mathematical journal
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• 제37권1호
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• pp.123-130
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• 2021

In this paper, we introduce the new concept of a cone metric-like space and consider some fixed point theorems for generalized contractive mappings under suitable conditions in cone metric-like spaces. Our results generalize and unify the several main results of [1, 2, 9].

• 대한수학회보
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• 제26권2호
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• pp.139-149
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• 1989

pp.Hartman and G. Stampacchia [6] proved the following theorem in 1966: If f:X.rarw. $R^{n}$ is a continuous map on a compact convex subset X of $R^{n}$ , then there exists $x_{0}$ ..mem.X such that $x_{0}$ , $x_{0}$ -x>.geq.0 for all x.mem.X. This remarkable result has been investigated and generalized by F.E. Browder [1], [2], W. Takahashi [9], S. Park [8] and others. For example, Browder extended this theorem to a map f defined on a compact convex subser X of a topological vector space E into the dual space $E^{*}$; see [2, Theorem 2]. And Takahashi extended Browder's theorem to closed convex sets in topological vector space; see [9, Theorem 3]. In Section 2, we obtain some variational inequalities, especially, generalizations of Browder's and Takahashi's theorems. The generalization of Browder's is an earlier result of the first author [8]. In Section 3, using Theorem 1, we improve and extend some known fixed pint theorems. Theorems 4 and 8 improve Takahashi's results [9, Theorems 5 and 9], respectively. Theorem 4 extends the first author's fixed point theorem [8, Theorem 8] (Theorem 5 in this paper) which is a generalization of Browder [1, Theroem 1]. Theorem 8 extends Theorem 9 which is a generalization of Browder [2, Theorem 3]. Finally, in Section 4, we obtain variational inequalities for multivalued maps by using Theorem 1. We improve Takahashi's results [9, Theorems 21 and 22] which are generalization of Browder [2, Theorem 6] and the Kakutani fixed point theorem [7], respectively.ani fixed point theorem [7], respectively.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.343-350
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• 2009

We prove the existence of common fixed point for multivalued maps satisfying general contractive type conditions.

• East Asian mathematical journal
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• 제18권2호
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• pp.225-233
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• 2002

In this paper, we obtain the common fixed point for fuzzy mappings satisfying an implicit relation. We improve earlier results of this line.

• 대한수학회보
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• 제21권2호
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• pp.55-60
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• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.

• 대한수학회논문집
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• 제25권4호
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• pp.583-607
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• 2010

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.433-440
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• 2002

In this paper, we first prove the existence of fixed points for fuzzy mappings that satisfy a certain contractive condition. Also, we give a fixed point theorem for generalized contractive fuzzy mapping by using Caristi's by fixed point theorem.

• 대한수학회보
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• 제50권1호
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• pp.305-320
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• 2013

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..