• The Pure and Applied Mathematics
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• v.29 no.4
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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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• v.28 no.4
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• pp.1087-1095
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• 2023

In this paper, the concept of a weighted b_ν(α)-metric space is introduced as a generalization of the b_ν(s)-metric space and ν-metric space. We prove some fixed point results of the Reich-type contraction in the weighted b_ν(α)-metric space. Furthermore, we generalize Reich's theorem by extending the result to a weighted b_ν(α)-metric space.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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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.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.719-729
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• 2023

In this article, we present a new notion called "extended metric spaces of type (φ, ρ)" as a generalization of extended b-metric spaces. Also, we establish a fixed point result of a Reich-type contraction on an extended metric space of type (φ, ρ). We also provide several examples to demonstrate the significance of the established results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.1-9
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• 2023

Our aim in this paper is to give some new proofs to fixed point theorems due to Abdou [1] for mappings satisfying Reich type contractions in modular metric spaces. We removed the restriction that ω satisfies the ∆₂-type condition imposed on the results of [1]. Furthermore, Lemma 2.6 of [1] which was crucial in the proofs of the results of [1] is not needed in the proofs of our results. Our method of proof is simpler and interesting.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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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.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.957-988
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• 2023

We define new classes of expansive-type mappings in the setting of modular 𝜔^G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔^G-complete modular 𝜔^G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.