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Article Citation - WoS: 3Citation - Scopus: 5Fixed Point Theorems for Generalized Contractions on gp-metric Spaces(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Salimi, PeymanIn this paper, we present two fixed point theorems on mappings, defined on GP-complete GP-metric spaces, which satisfy a generalized contraction property determined by certain upper semi-continuous functions. Furthermore, we illustrate applications of our theorems with a number of examples. Inspired by the work of Jachymski, we also establish equivalences of certain auxiliary maps in the context of GP-complete GP-metric spaces. MSC: 47H10, 54H25.Article Citation - WoS: 91Citation - Scopus: 109New Extension of p-metric Spaces With Some Fixed-Point Results on m-metric Spaces(Springer international Publishing Ag, 2014) Asadi, Mehdi; Karapinar, Erdal; Salimi, PeymanIn this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings.Article Citation - WoS: 19Citation - Scopus: 24Fixed Point Results for the Α-Meir Contraction on Partial Hausdorff Metric Spaces(Springeropen, 2013) Chen, Chi-Ming; Karapinar, ErdalThe purpose of this paper is to study fixed point theorems for a multi-valued mapping satisfying the alpha-Meir-Keeler contraction with respect to the partial Hausdorff metric H in complete partial metric spaces. Our result generalizes and extends some results in the literature.Article Citation - WoS: 12Citation - Scopus: 6A note on 'Modified proof of Caristi's fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210'(Springeropen, 2013) Aydi, Hassen; Karapinar, Erdal; Kumam, PoomIn this note, we emphasize that the proofs and statements of the main results of the paper 'Modified proof of Caristi's fixed point theorem on partial metric spaces' (Journal of Inequalities and Applications 2013, 2013:210) do not have any utility to use the partial metric. Hence, it has no contribution to either partial metric theory or Caristi-type fixed point problems.
