Some approximate fixed point theorems without continuity of the operator using auxiliary functions

Sumit Chandok; Arslan Hojjat Ansari; Tulsi Dass Narang

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 3, page 251-271
  • ISSN: 0862-7959

Abstract

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We introduce partial generalized convex contractions of order 4 and rank 4 using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in α -complete metric spaces and μ -complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained. Some examples are also provided to illustrate the main results and to show the usability of the given hypotheses.

How to cite

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Chandok, Sumit, Ansari, Arslan Hojjat, and Narang, Tulsi Dass. "Some approximate fixed point theorems without continuity of the operator using auxiliary functions." Mathematica Bohemica 144.3 (2019): 251-271. <http://eudml.org/doc/294623>.

@article{Chandok2019,
abstract = {We introduce partial generalized convex contractions of order $4$ and rank $4$ using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in $\alpha $-complete metric spaces and $\mu $-complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained. Some examples are also provided to illustrate the main results and to show the usability of the given hypotheses.},
author = {Chandok, Sumit, Ansari, Arslan Hojjat, Narang, Tulsi Dass},
journal = {Mathematica Bohemica},
keywords = {$\varepsilon $-fixed point; $\alpha $-admissible mapping; partial generalized convex contraction of order $4$ and rank $4$; $\alpha $-complete metric space},
language = {eng},
number = {3},
pages = {251-271},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some approximate fixed point theorems without continuity of the operator using auxiliary functions},
url = {http://eudml.org/doc/294623},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Chandok, Sumit
AU - Ansari, Arslan Hojjat
AU - Narang, Tulsi Dass
TI - Some approximate fixed point theorems without continuity of the operator using auxiliary functions
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 3
SP - 251
EP - 271
AB - We introduce partial generalized convex contractions of order $4$ and rank $4$ using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in $\alpha $-complete metric spaces and $\mu $-complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained. Some examples are also provided to illustrate the main results and to show the usability of the given hypotheses.
LA - eng
KW - $\varepsilon $-fixed point; $\alpha $-admissible mapping; partial generalized convex contraction of order $4$ and rank $4$; $\alpha $-complete metric space
UR - http://eudml.org/doc/294623
ER -

References

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