Research & Reviews: Discrete Mathematical Structures
Volume 11, Issue 1 (2024)
Table of contents
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Context of Different Graph Operations: Fibonacci Product Cordial Labeling of Herschel Graph
Abstract: The function φ: V (G) → {F1, F2,..., Fn}, where Fj is the jth Fibonacci number (j = 1,..., n), is said to be Fibonacci product cordial labeling if the induced function φ*: E (G) → {0, 1} defined by 𝜑∗ (𝑢𝑣) = (𝜑(𝑢)𝜑 (𝑣))(𝑚𝑜𝑑 2) meets the criterion |𝑒𝜑∗(0) – � �𝜑∗(1)| ≤ 1. A graph known as the Fibonacci product cordial graph is one that permits Fibonacci product …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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A Journey through Fixed Points and Non-expansive Mappings
Abstract: Fixed points in non-expansive mappings are elements that remain unchanged under the action of the mapping. Non-expansive mappings preserve or contract distances in a metric space. The rigorous proof of the Banach fixed-point theorem is presented at the outset of the paper, highlighting its fundamental significance. According to this theorem, every contraction mapping (a particular kind of non-expansive mapping that strictly reduces distances) has a single fixed point in a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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Comparative Evaluation of Fixed-Point Theorems Investigating Differences Among Conditions in Metric Spaces
Abstract: This paper provides a concise overview of metric spaces, their fundamental properties, and the idea of continuity as it pertains to these spaces, drawing parallels to uniform continuity and convergence. Also included is a review of previous research on metric space, its generalization, and practical outcomes from studies that utilized these spaces in various applications. We introduce a fixed point theorem for mixed monotone mappings in partially ordered metric spaces, …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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Optimal Homotopy Analysis Method (OHAM) For the Approximate Series Solution of Non-linear Partial Differential Equation
Abstract: In this article, we have used the Optimal Homotopy Analysis Method (OHAM), which is a basically semi-analytic method to solve differential equations. The ability for the user to choose the convergence control parameter, auxiliary linear operator, auxiliary function, and starting approximation is what sets apart the OHAM technique. We guaranteed the efficacy and efficiency of the procedure by fine-tuning the convergence control parameter. We solved a non-linear partial differential equation …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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A novel similarity measure for interval value picture fuzzy Environment and extended TOPSIS
Abstract: Correct decision-making is the most arduous task in our daily life. The decisions are hard to make in the multi-criteria decision-making (MCDM) problems due to ambiguous and unexpected information. In order to cope with such uncertainties in the data, a new decision-making approach has been developed using a newly defined similarity measure under the framework of interval-valued picture fuzzy set (IVPFS), as an extension of picture fuzzy sets (PFS). In …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 · pp. 1–10 Read article