We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunctio...

*Correspondence: [email protected] Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan Abstract We give characterizations of the contractive conditions, by using convergent sequences. Since we use a unified method, we can compare the contractive conditions very easily. We also discuss the contractive conditions of int...

In this paper, first we have established two sets of sufficient conditions for a TS-IF contractive mapping to have unique fixed point in a intuitionistic fuzzy metric space. Then we have defined ( ε , λ ) IF-uniformly locally contractive mapping and η− chainable space, where it has been proved that the ( ε , λ ) IF-uniformly locally contractive mapping possesses a fixed point.

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...

Abstract – A voltage-mode (VM), multi-input single-output (MISO) type multifunction biquad is proposed. It uses only one operational transresistance amplifier (OTRA) as the active element, while previously reported VM multifunction filters require more OTRAs. Proposed MISO type biquad configuration can realize all five different filter transfer functions. Theoretical results are verified with P...

It is shown that a composite Julia set generated by an infinite array of polynomial mappings is strongly analytic when regarded as a multifunction of the generating maps. An example of such a multifunction, the values of which have Hölder Continuity Property, is constructed. 1

We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4×4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4× 4 Hankel m...

This paper concerns a generalized equation defined by a closed multifunction between Banach spaces, and we employ variational analysis techniques to provide sufficient and/or necessary conditions for a generalized equation to have the metric subregularity (i.e., local error bounds for the concerned multifunction) in general Banach spaces. Following the approach of Ioffe [Trans. Amer. Math. Soc....

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to...

The problem of hardware-software partitioning for systems that are being designed as multifunction systems is addressed. Simulated annealing is known to generate very good solutions for most optimization problems, however the running time of this algorithm can be very high. We apply a modified simulated annealing approach to the partitioning problem resulting in a smaller search space, yet yiel...