Near fixed point theorems in near Banach spaces

Wu, Hsien-Chung

doi:10.3934/math.2023064

Cited by 2 publications

(1 citation statement)

References 5 publications

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“…1. Banach Hyperspace Sequences: [14] [15][16] Sequences of sets in the Banach hyperspace can be studied, and their convergence qualities under a selected norm can be examined. This is figuring out when a series of sets in the hyperspace converge to a limit set.…”

Section: Preliminariesmentioning

confidence: 99%

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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Section: Preliminariesmentioning

confidence: 99%

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

Savitha. S

2024

cana

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On a new nonlinear convex structure

Bejenaru,

Postolache

2023

MATH

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<abstract><p>In this work we start from near vector spaces, which we endow with some additional properties that allow convex analysis. The seminormed structure used here will also be improved by adding properties such as the null condition and null equality, thus resulting in a new type of space, which is still weaker than the conventional Banach structures: pre-convex regular near-Banach space. On the newly defined structure, we introduce the concept of uniform convexity and analyze several resulting properties. The major outcomes prove a remarkable resemblance to the classical properties resulting from uniform convexity on hyperbolic metric spaces or modular function spaces, including the famous Browder-Göhde fixed point theorem.</p></abstract>

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Near fixed point theorems in near Banach spaces

Cited by 2 publications

References 5 publications

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

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

On a new nonlinear convex structure

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