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8 articles for “contraction mapping”
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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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Intimate Mappings in Interval-Valued Fuzzy Metric Space: A Few Fixed-Point Findings
Abstract: The purpose of this study is to extend some previously established fixed point results for interval valued fuzzy metric space. For this objective, various contractive criteria with respect to an intimate mapping are applied. We employ intimate mapping in interval valued fuzzy metric space (IVFMS) to validate some well-known fixed point results. Our findings complement and generalize the recent findings of the common fixed point theorem for intimate mapping. The …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 16–23 Read article
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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
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Study of Proximity Points and Fixed Points
Abstract: This paper explores the concepts of proximity points and fixed points, which are fundamental in mathematical analysis and nonlinear functional analysis. Fixed-point theorems play a crucial role in optimization, game theory, differential equations, and dynamic systems. Proximity points, an extension of fixed points, provide a more generalized approach, allowing near-coincidence rather than exact identity. The study discusses classical fixed-point theorems, such as Banach’s contraction principle, Brouwer’s fixed-point theorem, and Schauder’s …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 28–31 Read article
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Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces
Abstract: This paper extends the Hicks contraction theory to multi-valued mappings within generalized b-Manger spaces, a class of metric-like structures that accommodate more flexible distance functions. By introducing new definitions, such as generalized admissibility conditions and weak compatibility in the multivalued sense, we provide a comprehensive analysis of how these contractions behave in broader topological and metric contexts. Our approach systematically generalizes classical contraction principles by relaxing conventional constraints, thereby broadening …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 1–05 Read article
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Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions
Abstract: Background: Fixed point theory in probabilistic metric spaces, particularly Menger spaces, has been a subject of intensive research due to its applications in nonlinear analysis and mathematical modeling. Traditional approaches often impose restrictive constraints on the defining properties of Menger spaces and limit the class of auxiliary functions in contractivity conditions Methods: We extend recent fixed point theorems in Menger spaces by: (1) introducing the notion of Menger PM-type spaces …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 1–6 Read article
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A Study of Fixed-Point and Best Proximity Point
Abstract: Fixed-point theory plays a fundamental role in nonlinear analysis and has significant applications in optimization, differential equations, and applied mathematics. This study investigates the existence and properties of fixed points and best proximity points for various classes of mappings defined on metric and normed spaces. While fixed-point results guarantee the existence of a point that remains invariant under a given mapping, such points may not exist when the mapping is …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 28–39 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