Kita and Yoneda showed that every Cauchy sequence with Orlicz norm r-converges in the Orlicz space considered as a ranked space, and however there exists an r-convergent sequence which is not a Cauchy sequence. We give an another proof and show that every sequence of points in every fundamental sequence r-converges

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We extend existence and uniqueness results of [4] for nonlinear integrodifferential equations of Volterra type between real locally complete vector spaces.

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Motivated by equations derived by Neri, Pointin-Lundgren and Joyce- Montgomery in the context of Onsager’s statistical theory of vortices, we study the blow-up properties of some sinh-Gordon type extensions of the standard mean field equation with exponential nonlinearity on two-dimensional compact surfaces.

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In the present paper, the convexity of fuzzy sets is generalized based on conjunctive aggregation functions, and the degree of the non-convexity of fuzzy sets is considered as an application of the generalized convexity. Then, the properties of the generalized convexity of fuzzy sets, and the properties of the degree of the nonconvexity of fuzzy sets with respect to operations are investigated.

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We give a characterization of ω1-strongly countable-dimensional metrizable spaces in terms of K-approximations. A characterization of locally finite-dimensional metrizable spaces is also obtained.

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The efficient Fisher information is defined by the Schur complement in the Fisher information. We statistically prove the concavity of the matrix function on the efficient Fisher information more sophisticated way than the previous one

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We construct several examples of Hausdorff (resp. regular) open-hereditarily irresolvable not hereditarily irresolvable or hereditarily irresolvable not submaximal spaces. Also, examples of separable or countable (connected or not) irresolvable spaces are constructed.

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Some inequalities for fractional integral operators on Morrey spaces are investigated by many researchers. In this paper, we extend and generalize some of them. More precisely, we show some inequalities concerning with g·Tρf, where Tρ is the generalized fractional integral operator and f and g are functions which belong to generalized Morrey spaces. We also compare our results and present counterexamples showing that our results are sharp.

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This paper deals with a two-person zero-sum search game called search allocation game (SAG) with a searcher and a target as players, taking account of false contacts. The searcher distributes his searching resource in a search space to detect the target and the target moves to evade the searcher. The searcher obtains a profit of target value on detection of target but expends cost for the search. The payoff of the game is the expected reward defined by obtained target value minus expended searching cost. The searcher’s strategy is denoted by a distribution plan about where and when he distributes his searching resource and the target strategy is the selection of a path to follow from some options. In the search operation, any sensor cannot get rid of false contacts caused by signal processing noises and real objects similar to the true target under noisy environment. On their happening, they make the searcher waste some time for investigation and interrupt the search operation for a while. There have been few researches dealing with the SAG with the false contacts. In this paper, we model the game with false contacts by a stochastic process and discuss a general procedure to derive an equilibrium point through a nonlinear programming method for a searcher’s best response to the target’s behavior.

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