Geodesic
Some approximate fixed point theorems without continuity of the operator using auxiliary functions
Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 251-271.

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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.
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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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. http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0095-17/

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