• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.293-306
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• 2022

In the present paper, we introduce the notation of 𝛿-convex rectangular metric spaces with the help of convex structure. We investigate fixed point results concerning Kannan-type contraction and Reich-type contraction in such spaces. We also propound an ingenious example in reference of given new notion.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.383-394
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• 2023

In this paper, we shall introduce the new notions of ω-orbital admissible mappings, ω-interpolative Kannan type contraction and ω-interpolative Ciric-Reich-Rus type contraction. In the setting of these new contractions, we will prove some fixed point theorems in bipolar metric spaces. Some existing results from literature are also deduced from our main results. Some examples are also provided to illustrate the theorems.

• 대한수학회논문집
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• 제27권2호
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• pp.265-277
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• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.809-822
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• 2018

In this paper, we introduce complex valued dislocated metric spaces. We prove Banach contraction principle, Kannan and Chatterjea type fixed point theorems in this new space. Moreover, we give some applications of the results to differential equations and iterated functions.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.581-596
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• 2024

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α⁺F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α⁺F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation.