Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions

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nThis is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.n

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Year : 2025 [if 2224 equals=””]04/10/2025 at 10:34 AM[/if 2224] | [if 1553 equals=””] Volume : 12 [else] Volume : 12[/if 1553] | [if 424 equals=”Regular Issue”]Issue : [/if 424][if 424 equals=”Special Issue”]Special Issue[/if 424] [if 424 equals=”Conference”][/if 424] 03 | Page : 1 6

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    Sulekha Tomar, Manoj Ughade,

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  1. Research Scholar, Assistant Professor, Department of Mathematics, Barkatullah University, Bhopal, Department of Mathematics, Institute for Excellence in Higher Education, Bhopal, Madhya Pradesh, Madhya Pradesh, India, India

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Abstract

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nBackground: 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 that avoids unnecessary constraints in the traditional definition, (2) considering a more general class of auxiliary functions in contractivity conditions, and (3) replacing the classical function t ↦ 1t − 1 with more appropriate and general functions Results: We establish several new fixed point theorems that generalize existing results in the literature. Our main theorem provides sufficient conditions for the existence and uniqueness of fixed points under weaker assumptions than previously required. We demonstrate that our auxiliary functions encompass a broader class of contractive mappings Conclusions: The proposed extensions significantly broaden the applicability of fixed point theorems in Menger spaces. We provide a concrete example where previous results cannot be applied, highlighting the necessity and utility of our generalizations. These results have potential applications in solving integral equations, optimization problems, and other areas of mathematical analysis.nn

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Keywords: Fixed point theorems; Menger PM-type spaces; probabilistic metric spaces; auxiliary functions; contractivity conditions; generalized contractions

n[if 424 equals=”Regular Issue”][This article belongs to Research & Reviews: Discrete Mathematical Structures ]

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[/if 424][if 424 equals=”Special Issue”][This article belongs to Special Issue under section in Research & Reviews: Discrete Mathematical Structures (rrdms)][/if 424][if 424 equals=”Conference”]This article belongs to Conference [/if 424]

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How to cite this article:
nSulekha Tomar, Manoj Ughade. [if 2584 equals=”][226 wpautop=0 striphtml=1][else]Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions[/if 2584]. Research & Reviews: Discrete Mathematical Structures. 30/09/2025; 12(03):1-6.

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nSulekha Tomar, Manoj Ughade. [if 2584 equals=”][226 striphtml=1][else]Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions[/if 2584]. Research & Reviews: Discrete Mathematical Structures. 30/09/2025; 12(03):1-6. Available from: https://journals.stmjournals.com/rrdms/article=30/09/2025/view=0

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[if 424 not_equal=””]Regular Issue[else]Published[/if 424] Subscription Review Article

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Volume 12
[if 424 equals=”Regular Issue”]Issue[/if 424][if 424 equals=”Special Issue”]Special Issue[/if 424] [if 424 equals=”Conference”][/if 424] 03
Received 05/09/2025
Accepted 22/09/2025
Published 30/09/2025
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Publication Time 25 Days

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