Browsing by Author "Khojasteh, Farshid"
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Article Citation Count: 59An approach to best proximity points results via simulation functions(Springer Basel Ag, 2017) Karapınar, Erdal; Khojasteh, Farshid; MathematicsIn this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.Article Citation Count: 4A note on fixed point results in complex-valued metric spaces(Springer international Publishing Ag, 2015) Karapınar, Erdal; Alsulami, Hamed H.; Karapinar, Erdal; Khojasteh, Farshid; MathematicsIn this paper, we prove that the fixed point results in the context of complex-valued metric spaces can be obtained as a consequence of corresponding existing results in the literature in the setting of associative metric spaces. In particular, we deduce that any complex metric space is a special case of cone metric spaces with a normal cone.Article Citation Count: 3ON SOME FIXED POINT RESULTS IN EXTENDED STRONG b-SPACES(int Center Scientific Research & Studies, 2018) Karapınar, Erdal; Karapinar, Erdal; Khojasteh, Farshid; MathematicsIn this paper, we propose a notion of a strong extended b-metric space and investigate the existence and uniqueness of a fixed point of certain operators.Article Citation Count: 56A Proposal to the Study of Contractions in Quasi-Metric Spaces(Hindawi Ltd, 2014) Karapınar, Erdal; Karapinar, Erdal; Khojasteh, Farshid; Roldan-Lopez-de-Hierro, Antonio-Francisco; MathematicsWe investigate the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces. Our results generalize and improve several recent results in literature.Article Citation Count: 5Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces(Hindawi Ltd, 2014) Karapınar, Erdal; Alsulami, Hamed H.; Karapinar, Erdal; Khojasteh, Farshid; MathematicsVery recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.Article Citation Count: 13A short note on C*-valued contraction mappings(Springeropen, 2016) Karapınar, Erdal; Agarwal, Ravi P.; Karapinar, Erdal; Khojasteh, Farshid; MathematicsIn this short note we point out that the recently announced notion, the C*-valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C*-valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.Article Citation Count: 21θ-Metric Space: A Generalization(Hindawi Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Radenovic, Stojan; MathematicsWe introduce the notion of theta-metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a theta-metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.