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This paper proposes a dynamic model for the spot foreign exchange rate which is governed by a standard Brownian motion and a stationary compound Poisson process in the domestic-real world. Using th...

In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.

In the real world, we introduce a dynamic model about the risky asset which is governed by Brownian motion, stationary compound Poisson process and its compensation process. By choosing Ess...

Classification of bone tumor plays an important role in treatment. As artificial diagnosis is in low efficiency, an automatic classification system can help doctors analyze medical images better. However, most existing methods cannot reach high classification accuracy on clinical images because of the high similarity between images. In this paper, we propose a super label guided convolutional neural network (SG-CNN) to classify CT images of bone tumor. Images with two hierarchical labels would be fed into the network, and learned by its two sub-networks, whose tasks are learning the whole image and focusing on lesion area to learn more details respectively. To further improve classification accuracy, we also propose a multi-channel enhancement (ME) strategy for image preprocessing. Owing to the lack of suitable public dataset, we introduce a CT image dataset of bone tumor. Experimental results on this dataset show our SG-CNN and ME strategy improve the classification accuracy obviously.

We prove the equivalence of the convergence of the Mann and multistep iterations with errors for uniformly continuous generalized weakΦ-pseduocontractive mappings in Banach spaces. We also obtain the convergence results of Mann and multistep iterations with errors. Our results extend and improve the corresponding results.

We prove the equivalence of the convergence of the Mann and Ishikawa iterations with errors for uniformly continuous generalized Φ-pseudocontractive mappings in normed linear spaces. Our results extend and improve the corresponding results of Xu, 1998, Kim et al., 2009, Ofoedu, 2006, Chidume and Zegeye, 2004, Chidume, 2001, Chang et al. 2002, Liu, 1995, Hirano and huang, 2003, C. E. Chidume and C. O. Chidume, 2005, and huang, 2007.

In this paper, we show the equivalence of convergence between the modified Mann and Ishikawa iterations with errors for an asymptotically pseudocontractive mapping under the condition of removing the bounded assumption. We also point out the problems of (Rhoades and Soltuz in J. Math. Anal. Appl. 283:681-688, 2003; Xue in Bull. Korean Math. Soc. 47(2):295-305, 2010; Xue in J. Math. Inequal. 4(3):345-354, 2010), extend and improve the results of (Zeng in Acta Math. Sin. 47(2):219-228, 2004).

In this paper, we establish some strong convergence theorems of the modified Ishikawa and Mann iterations with errors of uniformly L-Lipschitzian asymptotically pseudocontractive mappings in real Banach spaces. Our results not only provide the new proof method, but also extend the known corresponding results given in (Chang in Proc. Am. Math. Soc. 129:845-853, 2001; Chang et al. in Appl. Math. Lett. 22:121-125, 2009; Goebel and Kirk in Proc. Am. Math. Soc. 35:171-174, 1972; Ofoedu in J. Math. Anal. Appl. 321:722-728, 2006; Schu in J. Math. Anal. Appl. 158:407-413, 1991). In order to get some applications of our results, we also provide specific examples.

We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.

In this paper, under the new condition we show that the convergence of the modified Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitz asymptotically pseudocontractive mappings in real Banach spaces. Our results extend and improve the corresponding results of Zeng (Acta Math. Sin. 47:219-228, 2004).

Let D be a nonempty closed convex subset of an arbitrary uniformly smooth real Banach space E, and be a generalized Lipschitz Φ-hemi-contractive mapping with . Let , , , be four real sequences in and satisfy the conditions (i) as and ; (ii) . For some , let , be any bounded sequences in D, and be an Ishikawa iterative sequence with errors defined by (1.1). Then (1.1) converges strongly to the fixed point q of T. A related result deals with the operator equations for a generalized Lipschitz and Φ-quasi-accretive mapping. MSC:47H10.

The purpose of this paper is to characterize conditions for the convergence of the implicit Ishikawa iterative scheme with errors in the sense of Agarwal et al. (J. Math. Anal. Appl. 272:435-447, 2002) to a common fixed point of two ϕ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space.