TY - JOUR
T1 - New fixed point results of the sum of two operators in fuzzy metric spaces and their applications
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
U2 - 10.1186/s13663-025-00810-8
DO - 10.1186/s13663-025-00810-8
M3 - Article
AN - SCOPUS:105019326102
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 -