Invariant approximation for fuzzy nonexpansive mappings

Ismat Beg; Mujahid Abbas

Mathematica Bohemica (2011)

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

Abstract

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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.

How to cite

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Beg, 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 -

References

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