Fixed point theorems under conditional semicompatibility with control function
Abstract
The aim of the present paper is to generalize the elegant work of Pathak et al.[17] by using the new notion of “conditional semicompatibility”. The new notion is proper generalization of semi compatibility and weak semi compatibility and can be applicable on commuting and compatible maps. We used compatible mappings, commuting mappings and absorbing mappings to prove theorems which also include (E.A.) property. In the last section we show that the new notion is a necessary condition for the existence of common fixed points.
Copyright © 2013 A.S. Saluja, Mukesh Kumar Jain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. S. Saluja, M. K. Jain, Fixed point theorems under conditional semicompatibility with control function, Adv. Fixed Point Theory 3 (2013), 648–666.
BibTeX
@article{Saluja2013,
author = {Saluja, A.S. and Jain, Mukesh Kumar},
title = {Fixed point theorems under conditional semicompatibility with control function},
journal = {Adv. Fixed Point Theory},
volume = {3},
year = {2013},
pages = {648--666},
doi = {}
}