# Invariant approximation for fuzzy nonexpansive mappings

Mathematica Bohemica (2011)

- Volume: 136, Issue: 1, page 51-59
- ISSN: 0862-7959

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topBeg, Ismat, and Abbas, Mujahid. "Invariant approximation for fuzzy nonexpansive mappings." Mathematica Bohemica 136.1 (2011): 51-59. <http://eudml.org/doc/197013>.

@article{Beg2011,

abstract = {We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all $t$-best approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric space is proved. Our results extend, generalize and unify various known results in the existing literature.},

author = {Beg, Ismat, Abbas, Mujahid},

journal = {Mathematica Bohemica},

keywords = {fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping; fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping},

language = {eng},

number = {1},

pages = {51-59},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Invariant approximation for fuzzy nonexpansive mappings},

url = {http://eudml.org/doc/197013},

volume = {136},

year = {2011},

}

TY - JOUR

AU - Beg, Ismat

AU - Abbas, Mujahid

TI - Invariant approximation for fuzzy nonexpansive mappings

JO - Mathematica Bohemica

PY - 2011

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 136

IS - 1

SP - 51

EP - 59

AB - We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all $t$-best approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric space is proved. Our results extend, generalize and unify various known results in the existing literature.

LA - eng

KW - fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping; fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping

UR - http://eudml.org/doc/197013

ER -

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