Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph

BALOG, LASZLO; Berinde, Vasile

doi:10.37193/cjm.2016.03.05

Cited by 11 publications

(3 citation statements)

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“…These are only some of the many reasons why Kannan contractions and generalizations of Kannan mappings play a particularly important role in fixed point theory and nonlinear analysis and attracted a rather important research work in the last decades, see [2], [5], [10], [14], [22], [24], [25], [32], [34], [35], [37]- [39], [41]- [52] and [53] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems

Berinde¹,

Pačurar²

2019

Preprint

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The aim of this paper in to introduce a large class of mappings, called enriched Kannan mappings, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for Kransnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces. We then extend further these mappings to the class of enriched Bianchini mappings. Examples to illustrate the effectiveness of our results are also given. As applications of our main fixed point theorems, we present two Kransnoselskij projection type algorithms for solving split feasibility problems and variational inequality problems in the class of enriched Kannan mappings and enriched Bianchini mappings, respectively.

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Section: Introductionmentioning

confidence: 99%

Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems

Berinde¹,

Pačurar²

2019

Preprint

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“…This expansion provides opportunities to examine fixed point attributes in spaces that have both metric and graph-theoretic properties; it also indicates a more nuanced understanding of the interactions between points. The possible applicability of this extension to problems where the presence of a graph structure poses difficulties for the classic Banach contraction principle demonstrate the significance of this work [1] [20].…”

Section: Introductionmentioning

confidence: 89%

Theorems for Near Stable Points on a Near Banach Space Furnished with Graph

Savitha. S

2024

cana

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The paper introduces a novel method for defining the graph associated with a near Banach space. In mathematics, a graph typically represents relationships between objects. Here, it seems the graph is being defined in the context of a near Banach space, which is a generalization of Banach spaces allowing the norm to take infinite values. An iteration function is utilized to define the subgraph of the graph associated with the near Banach space. This subgraph likely captures specific properties or relationships within the original graph. The paper presents near-fixed point theorems by well-known math- ematicians such as Banach, Kannan, Chatterja, and Ciric [2][18][7][9]. These theorems deal with the existence of points that are approximately fixed under certain mappings or operations. The near-fixed point theorems mentioned are obtained or derived using the new approach introduced for defining the graph and its subgraph associated with the near Banach space [20]. This suggests that the new approach is effective in providing a framework for proving these theorems or extending their applicability to near Banach spaces. The paper discusses a fresh method for defining the graph of a near Banach space, employs an iteration function to define its subgraph, and then demonstrates the utility of this approach by deriving near-fixed point theorems by eminent mathemati- cians in the field [14][15[16].

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“…Later on, Alfuraidan and Khamsi [1] introduced the notion of multi-valued G-nonexpansive mappings and proved the existence of fixed points for such kind of mappings in hyperbolic metric spaces. Since then, the fixed point results in several kinds of metric spaces endowed with graphs have been developed and many papers have appeared, see, e.g., [2,5,7,10,23,26,32,35,36,38].…”

Section: Introductionmentioning

confidence: 99%

Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

Kaewkhao¹,

Klangpraphan²,

Panyanak³

2021

CJM

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"In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and \Delta-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed."

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Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph

Cited by 11 publications

References 0 publications

Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems

Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems

Theorems for Near Stable Points on a Near Banach Space Furnished with Graph

Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

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