• 대한수학회보
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• 제33권4호
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• pp.565-585
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• 1996

In 1976, Caristi [1] established a celebrated fixed point theorem in complete metric spaces, which is a very useful tool in the theory of nonlinear analysis. Since then, several generalizations of the theorem were given by a number of authors: for instances, generalizations for single-valued mappings were given by Downing and Kirk [4], Park [11] and Siegel [13], and the multi-valued versions of the theorem were obtained by Chang and Luo [3], and Mizoguchi and Takahashi [10].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.237-246
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• 2016

Ebadian et al. proved the Hyers-Ulam stability of bimultipliers and Jordan bimultipliers in C*-ternary algebras by using the fixed point method. Under the conditions in the main theorems for bimultipliers, we can show that the related mappings must be zero. Moreover, there are some mathematical errors in the statements and the proofs of the results. In this paper, we correct the statements and the proofs of the results, and prove the corrected theorems by using the direct method.

• East Asian mathematical journal
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• 제28권1호
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• pp.63-71
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• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.461-475
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• 2024

The concept of an extension α-F-contraction and it's modified counterpart represents an advancement in the theory of metric space contractions. Through our study of the contraction principles and it's relationship to extension and modified extension, we found different conditions somewhat lengthy. In our paper, we create a development of the conditions for the extension of α-F-contraction and a modified α-F-contraction by reducing the conditions and make them easier. Our propose conditions are notably simple and effective. They serve as the foundation for proving theorems and solving examples that belong to our study. Moreover, they have remarkable significance in the condition of mathematical analysis and problem-solving. Thus, we find that these new conditions that we mention in the definitions achieve what is require and through them, we choose λ = 1 and we choose λ ∈ (0, 1) to clarify our ideas.

• Kyungpook Mathematical Journal
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• 제32권2호
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• pp.203-216
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• 1992

• East Asian mathematical journal
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• 제12권2호
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• pp.243-251
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• 1996

• East Asian mathematical journal
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• 제8권1호
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• pp.91-102
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• 1992

• East Asian mathematical journal
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• 제11권1호
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• pp.73-80
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• 1995

• 대한수학회보
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• 제52권3호
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• pp.789-807
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• 2015

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.