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Keywords = enriched Suzuki mapping

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21 pages, 363 KB  
Article
New α-ɛ-Suzuki-Type Contraction Mapping Methods on Fractional Differential and Integral Equations
by Keyu Zhang, Meltem Erden Ege, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Ozgur Ege and Jiafa Xu
Fractal Fract. 2025, 9(11), 692; https://doi.org/10.3390/fractalfract9110692 - 27 Oct 2025
Viewed by 915
Abstract
This paper introduces novel formulations in the framework of αE-contractions within the context of admissible mappings. We establish new fixed point theorems for αE-Suzuki-type contractions, thereby generalizing and extending the foundational work of Hossein Piri and Poom [...] Read more.
This paper introduces novel formulations in the framework of αE-contractions within the context of admissible mappings. We establish new fixed point theorems for αE-Suzuki-type contractions, thereby generalizing and extending the foundational work of Hossein Piri and Poom Kumam. The principal objective of this research is to investigate the existence and uniqueness of solutions to a class of integral equations by leveraging fixed point methodologies in complete metric spaces. By developing these advanced αE-contraction concepts and analyzing their implications for admissible mappings, this work contributes to the theoretical advancement of fixed point theory. To support our new definition, we illustrate examples. The results demonstrate the efficacy of this approach for addressing nonlinear problems in analysis, specifically enriching the methodology for solving integral equations. The overarching aim is to consolidate the theoretical underpinnings and provide a rigorous analytical framework for the application of αE-contraction mappings, thereby fostering further progress in mathematical analysis. Full article
17 pages, 285 KB  
Article
Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
by Doaa Filali, Fahad Maqbul Alamrani, Esmail Alshaban, Adel Alatawi, Amid Yousef Alanazi and Faizan Ahmad Khan
Axioms 2025, 14(6), 426; https://doi.org/10.3390/axioms14060426 - 30 May 2025
Cited by 2 | Viewed by 1118
Abstract
This paper investigates the approximation of fixed points for mappings that satisfy the enriched (C) condition using a modified iterative process in a Banach space framework. We first establish a weak convergence result and then derive strong convergence theorems under suitable assumptions. To [...] Read more.
This paper investigates the approximation of fixed points for mappings that satisfy the enriched (C) condition using a modified iterative process in a Banach space framework. We first establish a weak convergence result and then derive strong convergence theorems under suitable assumptions. To illustrate the applicability of our findings, we present a numerical example involving mappings that satisfy the enriched (C) condition but not the standard (C) condition. Additionally, numerical computations and graphical representations demonstrate that the proposed iterative process achieves a faster convergence rate compared to several existing methods. As a practical application, we introduce a projection based an iterative process for solving split feasibility problems (SFPs) in a Hilbert space setting. Our findings contribute to the ongoing development of iterative processes for solving optimization and feasibility problems in mathematical and applied sciences. Full article
(This article belongs to the Special Issue Fixed-Point Theory and Its Related Topics, 5th Edition)
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11 pages, 258 KB  
Article
On Enriched Suzuki Mappings in Hadamard Spaces
by Teodor Turcanu and Mihai Postolache
Mathematics 2024, 12(1), 157; https://doi.org/10.3390/math12010157 - 3 Jan 2024
Cited by 4 | Viewed by 1868
Abstract
We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the setting and the class of involved operators. [...] Read more.
We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the setting and the class of involved operators. More accurately, Hilbert spaces are particular Hadamard spaces, while enriched Suzuki nonexpansive mappings are natural generalizations of enriched nonexpansive mappings. Next, enriched Suzuki nonexpansive mappings naturally contain Suzuki nonexpansive mappings in Hadamard spaces. Besides technical lemmas, the results of this paper deal with (1) the existence of fixed points for enriched Suzuki nonexpansive mappings and (2) Δ and strong (metric) convergence of Picard iterates of the α-averaged mapping, which are exactly Krasnoselskij iterates for the original mapping. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
12 pages, 277 KB  
Article
Approximation of Fixed Points for Enriched Suzuki Nonexpansive Operators with an Application in Hilbert Spaces
by Kifayat Ullah, Junaid Ahmad, Muhammad Arshad and Zhenhua Ma
Axioms 2022, 11(1), 14; https://doi.org/10.3390/axioms11010014 - 29 Dec 2021
Cited by 13 | Viewed by 2904
Abstract
In this article, we introduce the class of enriched Suzuki nonexpansive (ESN) mappings. We show that this new class of mappings properly contains the class of Suzuki nonexpansive as well as the class of enriched nonexpansive mappings. We establish existence of fixed point [...] Read more.
In this article, we introduce the class of enriched Suzuki nonexpansive (ESN) mappings. We show that this new class of mappings properly contains the class of Suzuki nonexpansive as well as the class of enriched nonexpansive mappings. We establish existence of fixed point and convergence of fixed point in a Hilbert space setting under the Krasnoselskii iteration process. One of the our main results is applied to solve a split feasibility problem (SFP) in this new setting of mappings. Our main results are a significant improvement of the corresponding results of the literature. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
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