New fixed point results of the sum of two operators in fuzzy metric spaces and their applications

A. Ashwinidevi; Poonguzali Govindaraju; Sabri T.M. Thabet; Imed Kedim; Ashish Rayal

doi:10.1186/s13663-025-00810-8

New fixed point results of the sum of two operators in fuzzy metric spaces and their applications

A. Ashwinidevi
, Poonguzali Govindaraju
, Sabri T.M. Thabet
, Imed Kedim
, Ashish Rayal

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the fuzzy fixed point theory literature, discussions of fixed points have been limited to maps involving a single function. Till now, the presence of a fixed point for the sum of two fuzzy operators is an open question, and in our study, we have affirmatively answered that question. The paper is primarily concerned with the solution of the operator equation, where one of the operators is a fuzzy compact linear operator and the other is a variety of contraction and contractive maps. At the end, we apply the main findings to an integral equation.

Original language	English
Article number	30
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2025
Issue number	1
DOIs	https://doi.org/10.1186/s13663-025-00810-8
State	Published - Dec 2025

Keywords

Fuzzy compact linear operator
Fuzzy contractive mapping
Generalized Fuzzy contractive mapping
χ-set contraction

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10.1186/s13663-025-00810-8

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abstract = "In the fuzzy fixed point theory literature, discussions of fixed points have been limited to maps involving a single function. Till now, the presence of a fixed point for the sum of two fuzzy operators is an open question, and in our study, we have affirmatively answered that question. The paper is primarily concerned with the solution of the operator equation, where one of the operators is a fuzzy compact linear operator and the other is a variety of contraction and contractive maps. At the end, we apply the main findings to an integral equation.",

keywords = "Fuzzy compact linear operator, Fuzzy contractive mapping, Generalized Fuzzy contractive mapping, χ-set contraction",

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AU - Ashwinidevi, A.

AU - Govindaraju, Poonguzali

AU - Thabet, Sabri T.M.

AU - Kedim, Imed

AU - Rayal, Ashish

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/12

Y1 - 2025/12

N2 - In the fuzzy fixed point theory literature, discussions of fixed points have been limited to maps involving a single function. Till now, the presence of a fixed point for the sum of two fuzzy operators is an open question, and in our study, we have affirmatively answered that question. The paper is primarily concerned with the solution of the operator equation, where one of the operators is a fuzzy compact linear operator and the other is a variety of contraction and contractive maps. At the end, we apply the main findings to an integral equation.

AB - In the fuzzy fixed point theory literature, discussions of fixed points have been limited to maps involving a single function. Till now, the presence of a fixed point for the sum of two fuzzy operators is an open question, and in our study, we have affirmatively answered that question. The paper is primarily concerned with the solution of the operator equation, where one of the operators is a fuzzy compact linear operator and the other is a variety of contraction and contractive maps. At the end, we apply the main findings to an integral equation.

KW - Fuzzy compact linear operator

KW - Fuzzy contractive mapping

KW - Generalized Fuzzy contractive mapping

KW - χ-set contraction

UR - https://www.scopus.com/pages/publications/105019326102

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DO - 10.1186/s13663-025-00810-8

M3 - Article

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SN - 1687-1820

VL - 2025

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

IS - 1

M1 - 30

ER -

New fixed point results of the sum of two operators in fuzzy metric spaces and their applications

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Keywords

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