arXiv subjects
Publications and source records attributed to Erdal Karapinar.
In this work, partial answers to Reich, Mizoguchi and Takahashi, and Amini-Harandi's conjectures are presented via a light version of Caristi's fixed point theorem. Moreover, we introduce that many of known fixed point theorem can easily derived from the Caristi's theorem. Finally, existence of bounded solutions of a functional equation is studied.
In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric spaces. Moreover, some partial answers to some known open problems are given via Caristi's corollaries. Finally, existence of bounded solutions of a functional equation is studied to support our results.
In this paper, using a more generalized inequality instead of triangle inequality, the notion of θ-metric space is introduced. Some important properties of induced topology by such spaces are presented. Also, Banach and Caristi type fixed point in such spaces are proved.
The notion of coupled fixed point is introduced in by Bhaskar and Lakshmikantham in [2]. Very recently, the concept of tripled fixed point is introduced by Berinde and Borcut [1]. In this manuscript, by using the mixed g monotone mapping, some new quartet fixed point theorems are obtained. We also give some examples to support our results.