In this paper, a new monotonicity, M(·, ·)-monotonicity,is introduced in Banach spaces, and the resolvent operator of an M(·, ·)monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·, ·)monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the conver...

In this paper, we study M-iterative scheme in the new context of multi-valued generalized ?-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a example ?-nonexpasive connect M iterative and other well known schemes with example, to show numerical efficiency results. Our results improve extend many existing current literature.

Let Bc denote the real-valued functions continuous on the extended real line and vanishing at −∞. Let Br denote the functions that are left continuous, have a right limit at each point and vanish at −∞. Define Ac to be the space of tempered distributions that are the nth distributional derivative of a unique function in Bc. Similarly with A n r from Br. A type of integral is defined on distribu...

We investigate which represented spaces enjoy the fixed-point property, is property that every continuous multi-valued function has a fixed-point. study basic theory of this notion and its uniform version. provide complete characterization countable-based T0-spaces with showing they are exactly pointed ω-continuous dcpos. prove whose lattice open sets enjoys countably-based spaces. While role p...

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes Incomplete Information semiuniform Feller transition probabilities. The important feature these models is that their classic reduction to Completely Observable belief states preserves continuity Under mild assumptions on cost functions, optimal policies exi...

Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoidM andQ-enriched categories are introduced for quantales L andQ, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, la...

A Hausdorff topological space X is van der Waerden if for every sequence (xn)n∈ω in X there is a converging subsequence (xn)n∈A where A ⊆ ω contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (xn)n∈ω in X there is an IP-converging subsequence (xn)n∈FS(B) for some infinite B ⊆ ω. We show that the continuum hypothesis implies th...