Geodesic
Some approximate fixed point theorems without continuity of the operator using auxiliary functions
Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 251-271 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\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.
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.
DOI : 10.21136/MB.2018.0095-17
Classification : 47H10, 54H25
Keywords: $\varepsilon $-fixed point; $\alpha $-admissible mapping; partial generalized convex contraction of order $4$ and rank $4$; $\alpha $-complete metric space 
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     title = {Some approximate fixed point theorems without continuity of the operator using auxiliary functions},
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Chandok, Sumit; Ansari, Arslan Hojjat; Narang, Tulsi Dass. Some approximate fixed point theorems without continuity of the operator using auxiliary functions. Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 251-271. doi: 10.21136/MB.2018.0095-17

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