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Citation - WoS: 26
Citation - Scopus: 26
Coupled Coincidence Points for Mixed Monotone Operators in Partially Ordered Metric Spaces
(Springer Heidelberg, 2012) Karapinar, Erdal; Karapınar, Erdal; Van Luong, Nguyen; Thuan, Nguyen Xuan; Karapınar, Erdal; Mathematics; Mathematics
In this paper, we give and prove some coupled coincidence point theorems for mappings F : X x X -> X and g : X -> X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65: 1379-1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4): 16-24, 2010), Harjani et al. (Nonlinear Anal 74: 1749-1760, 2011) and Choudhury et al. (Ann Univ Ferrara 57: 1-16, 2011). We also give some examples to illustrate our results.
Citation - WoS: 30
Citation - Scopus: 37
Θ-Metric Space: a Generalization
(Hindawi Ltd, 2013) Khojasteh, Farshid; Karapınar, Erdal; Karapinar, Erdal; Radenovic, Stojan; Karapınar, Erdal; Mathematics; Mathematics
We 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.