The basics of a block oriented fractal image coder, are described. The output of the coder is an IFS (Iterated Function System) code, which describes the image as a xed-point of a contractive transformation. A new hierarchical interpretation of the IFS code, which relates diierent scales of the xed-point to the code, is presented and proved. The proof is based on nding a function of a continuou...

In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point p...

In this paper we study self-similar solutions for nonlinear Schrödinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrödinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in B...

This paper investigates the use of fractal coding for image compression and reconstruction. The encoder exploits self-similarity of the image at different resolutions, mapping larger blocks of the image to similar smaller blocks through a series of contractive transformations. The decoder can apply these transformations iteratively to any image, and recover the original. We show that varying th...

We consider a scalar conservation law with a discontinuous flux function. The fluxes are non-convex, have multiple points of extrema and can have arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at the interface. We show that the entropy solutions with respect to each choice of interface connection exist and form a contract...

We introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping T in the intermediate sense which is necessarily lipschitzian. We establish strong convergence theorem for such method. The result extend and improve the recent ones announced by Inchan and Nammanee, Inchan and concern result of Takahashi, Takeuchi and Kubota [Strong convergence...

Fixed point and coincidence results are presented for multivalued generalized n -weak contractive mappings on complete metric spaces, where N: [0, +4) ÷ [0, +4) is a lower semicontinous function with N (0) = 0 and N (t) > 0 for all t > 0. Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969) and DaTer and Kaneko (1995). Branciari (2002) gave a...

We describe here a new mapping method able to find out connectivity traces among variables thanks to an artificial adaptive system, the Auto Contractive Map (AutoCM), able to define the strength of the associations of each variable with all the others in a dataset. After the training phase, the weights matrix of the AutoCM represents the map of the main connections between the variables. The ex...

A new hybrid wavelet-fractal coder (WFC) for image compression is proposed in this research. We show that the application of contractive mapping for interscale wavelet prediction in the wavelet domain o ers bit rate savings in some regions. The prediction residue is then quantized and encoded by traditional wavelet coders. WFC allows the exibility to choose either direct coding of wavelet coe c...