In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak convergence theorem, we prove a weak convergence theorem of Mann’s type for finding a common element of finite sets in a Banach space.

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In this note we state an extension of a Cafiero’s criterion and some Dieudonn´e convergence type theorems for semigroup-valued finitely additive functions by means of the relationships between regularity and exhaustivity.

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In this paper, we characterize the class of ω₁-strongly countable-dimensional metrizable spaces by a special metric. A characterization of locally finite-dimensional metrizable spaces is also obtained.

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In this paper we give a positive answer for the following problem: Assume that 2 < r < s < +∞. Is it possible to find a sequence space λ which is proper subset of 1 and a linear map T between normed spaces E and F such that T is s-quasi-λ-nuclear which is not r-quasi-λ-nuclear? [2]

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An objective of the competitive facility location problems is mainly to maximize customers using her/his facilities. This paper proposes a new multiobjective competitive facility location problem by adding another new objective about the convenience for customers. A solution algorithm based upon the goal programming is proposed for the formulated multiobjective problem. It is shown the result of applying the solution algorithm to numerical examples for the multiobjective competitive facility location problem.

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In this paper we discuss the second order power properties of empirical likelihood for stationary processes. The asymptotic distribution of empirical likelihood ratio statistics under a sequence of local alternatives is given.

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In this paper we define the concepts of good H-congruence relations, weak positive implicative subsets, positive implicative subsets, weak maximal hyper MVfilters and maximal hyper MV-filters in hyper MV-algebras. We then use some of the above notions to define quotient hyper MV-algebras. We state and prove some related theorems with appropriate results. In particular, we define the notion of the fundamental relation with its basic properties.

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In this note first we define the notions of positive implicative hyper Kideals of types 1, 2,..., 26, 27 . Also we define the notions of commutative hyper K-ideals of types 1, 2, ...,8, 9. Then we give many examples to show that these notions are different together. Finally we prove some theorems and obtain some related results . In particular we determine the relationships between the implicative hyper K-ideals and commutative hyper K-ideals of a hyper K-algebra of order 3, which satisfies the simple condition.

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