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Article Citation - WoS: 13Citation - Scopus: 19A Note on Caristi-Type Cyclic Maps: Related Results and Applications(Springer international Publishing Ag, 2013) Du, Wei-Shih; Karapinar, ErdalIn this note, we first introduce the concept of Caristi-type cyclic map and present a new convergence theorem and a best proximity point theorem for Caristi-type cyclic maps. It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property. Some best proximity point results and convergence theorems in the literature have been derived from our main results. Consequently, the presented results improve, extend and generalize some of the existence results on the topic.Article Citation - WoS: 34Citation - Scopus: 48A Note on Cone b-metric and Its Related Results: Generalizations or Equivalence?(Springer international Publishing Ag, 2013) Du, Wei-Shih; Karapinar, ErdalVery recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them.Editorial New Contribution To the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems(Hindawi Publishing Corporation, 2013) Du, Wei-Shih; Karapinar, Erdal; Lin, Lai-Jiu; Lee, Gue Myung; Tanaka, Tamaki[No Abstract Available]Article Citation - WoS: 5Citation - Scopus: 7Some Simultaneous Generalizations of Well-Known Fixed Point Theorems and Their Applications To Fixed Point Theory(Mdpi, 2018) Du, Wei-Shih; Karapinar, Erdal; He, ZhenhuaIn this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan's fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The presented results not only unify and generalize the existing results, but also yield several new fixed point theorems, which are different from the well-known results in the literature.
