Mathematica Bohemica, Vol. 144, No. 3, pp. 251-271, 2019


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

Sumit Chandok, Arslan Hojjat Ansari, Tulsi Dass Narang

Received April 09, 2017.   Published online September 25, 2018.

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.
Keywords:  $\varepsilon$-fixed point; $\alpha$-admissible mapping; partial generalized convex contraction of order $4$ and rank $4$; $\alpha$-complete metric space
Classification MSC:  47H10, 54H25


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Affiliations:   Sumit Chandok (corresponding author), School of Mathematics, Thapar Institute of Engineering & Technology, P.O. Box 32, Bhadson Road, Patiala 147-004, Punjab, India, e-mail: sumit.chandok@thapar.edu; Arslan Hojjat Ansari, Department of Mathematics, Karaj Branch, Islamic Azad University, Imam Ali Complex, Moazen Blvd, Karaj,Tehran, Iran, e-mail: mathanalsisamir4@gmail.com; Tulsi Dass Narang, Department of Mathematics, Guru Nanak Dev University, Grand Trunk Road, Off NH 1, Amritsar, Punjab-143005, India, e-mail: tdnarang1948@yahoo.co.in


 
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