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Access Right: info:eu-repo/semantics/openAccessInstitution Author: Karapınar, Erdal (16678995500)

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Now showing 1 - 3 of 3
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    Article
    Citation - WoS: 23
    Citation - Scopus: 31
    A Discussion on "α-Ψ Contraction Type Mappings "
    (Univ Nis, Fac Sci Math, 2014) Karapinar, Erdal
    In this paper we discuss the subadditivity property of some auxiliary functions which have been used to generalize the contractive conditions on maps. Our results show that this property is not required in many cases and therefore, can be removed. We emphasize that in several papers (see e.g.[1]-[11]) dealing with such contraction mappings, the hypotheses of the main theorems can be restated in the light of our results.
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    Article
    Citation - WoS: 57
    Citation - Scopus: 43
    On Best Proximity Point of Ψ-Geraghty Contractions
    (Springer international Publishing Ag, 2013) Karapinar, Erdal; Erhan, Inci M.
    Very recently, Caballero, Harjani and Sadarangani (Fixed Point Theory Appl. 2012: 231, 2012) observed some best proximity point results for Geraghty contractions by using the P-property. In this paper, we introduce the notion of psi-Geraghty contractions and show the existence and uniqueness of the best proximity point of such contractions in the setting of a metric space. We state examples to illustrate our result.
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    Article
    Citation - WoS: 8
    Citation - Scopus: 9
    Edelstein Type Fixed Point Theorems
    (Springer international Publishing Ag, 2012) Karapinar, Erdal
    In this manuscript, we investigate certain conditions that imply the existence of fixed points for almost contraction mappings defined on compact metric spaces. Furthermore we introduce a criteria establishing the uniqueness of fixed points for the mentioned operators. As a result we obtain generalized results by unifying some recent related fixed point theorems on the topic.