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This paper examines smoothness attributes of probability measures on lattices which indicate regularity, and then discusses weaker forms of regularity; specifically, weakly regular and vaguely regular. They are obtained from commonly used outer measures, and we study them mainly for the case ofM(ℒ)or for those components ofM(ℒ)with added smoothness prerequisites. This is a generalization of many concepts presented in my earlier paper (see [1]).

This paper deals with a class of algebraic hyperstructures called semihypergroups, which are a generalization of semigroups. In this paper, we introduce pure hyperradical of a hyperideal in a semihypergroup with zero element. For this purpose, we define pure, semipure, and other related types of hyperideals and establish some of their basic properties in semihypergroups.

This paper is a comprehensive study of a certain generalization of Whitney-type and Stirling-type numbers which unifies the classical Whitney numbers, the translated Whitney numbers, the classical Stirling numbers, and the noncentral Stirling (orr-Stirling) numbers. Several identities, applications, and occurrences are also presented.

Real hypersurfaces satisfying the conditionϕl=lϕ(l=R(·,ξ)ξ)have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective planeCP2satisfying a generalization ofϕl=lϕunder an additional restriction on a specific function.

In 1941, F. B. Jones introduced aposyndesis, which generalizes the concept of semi-local connectedness defined earlier by G. T. Whyburn (1942), in the study of continuum theory. Using Jones's idea, D. A. John (1993) defined abcohesiveness as a generalization of aposyndesis and studied theA-sets in abcohesive spaces. In this paper, some properties of abcohesive spaces are studied and a number of results by B. Lehman (1976) and Whyburn (1942, 1968) are generalized; sufficient conditions for the existence of two nodal sets are established as well.

We consider the fuzzification of the notion of implicative hyper BCK-ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative hyper BCK-ideal. We establish a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hyper BCK-ideal. Finally, we introduce the notion of hyper homomorphisms of hyper BCK-algebras, and discuss related properties. 2000 Mathematics Subject Classification: 06F35, 03G25, 20N20, 03B52. 1. Introduction. The hyper structure theory (called also multialgebras) is introduced in 1934 by Marty [5] at the 8th Congress of Scandinavian Mathematicians. Around the 40’s, several authors worked on hypergroups, especially in France and in the United States, but also in Italy, Russia, and Japan. Over the following decades, many important results appeared, but above all since the 70’s onwards the most luxuriant flourishing of hyper structures has been seen. Hyper structures have many applications to several sectors of both pure and applied sciences. Jun et al. [4] applied the hyper structures to BCK-algebras, and introduced the concept of a hyper BCK-algebra which is a generalization of a BCK-algebra, and investigated some related properties. They also introduced the notion of a hyper BCK-ideal and a weak hyper BCK-ideal, and gave relations between hyper BCK-ideals and weak hyper BCK-ideals. Jun and Xin [1] considered the fuzzification of the notion of a (weak, strong, reflexive) hyper BCK-ideal, and investigated the relations among them. In this paper, we deal with the fuzzification of the notion of implicative hyper BCK-ideals. We show that every fuzzy implicative hyper BCK-ideal is a fuzzy hyper BCK-ideal, but not converse. We provide a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hyper BCK-ideal. Using the notion of level subsets of a fuzzy set, we give a characterization of a fuzzy implicative hyper BCK-ideal. We introduce the concept of hyper homomorphisms of hyper BCK-algebras, and we show that the hyper homomorphic preimage of a fuzzy implicative hyper BCK-ideal is also a fuzzy implicative hyper BCK-ideal.

The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.

In this paper, we characterize all the functions that attain their Flett mean value at a particular point between the endpoints of the interval under consideration. These functions turn out to be cubic polynomials and thus, we also characterize these.

Recently, in 2013, we proved that certain presentations present the Dunwoody3-manifold groups. Since the Dunwoody3-manifolds do not have a unique Heegaard diagram, we cannot determine a unique group presentation for the Dunwoody3-manifolds. It is well known that every(1,1)-knots in a lens space can be represented by the set𝒟of the 4-tuples(a,b,c,r)(Cattabriga and Mulazzani (2004); S. H. Kim and Y. Kim (2012, 2013)). In particular, to determine a unique Heegaard diagram of the Dunwoody3-manifolds, we proved the fact that the certain subset of𝒟representing all2-bridge knots of(1,1)-knots is determined completely by using the dual and mirror(1,1)-decompositions (S. H. Kim and Y. Kim (2011)). In this paper, we show how to obtain the dual and mirror images of all elements in𝒟as the generalization of some results by Grasselli and Mulazzani (2001); S. H. Kim and Y. Kim (2011).

Letd(k)be defined as the least positive integernfor whichpn+1<2pn−k. In this paper we will show that fork≥286664, thend(k)

The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.

In this paper we present an extension of Bauer's work about u-means. We consider a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible function ϕ(x). This construction allows us to define (u,ϕ)-means. When ϕ(x)=x, the (u,ϕ)-means are the u-means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases.

1. Introduction. In this paper, we study the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for impulsive functionaldifferential evolution equation. Such problems arise in some physical applications as a natural generalization of the classical initial value problems. The results for semilinear functional-differential evolution nonlocal problem [2] are extended for the case of impulse effect. We consider the nonlocal Cauchy problem in the form

In 1995, Faith and Menal have established theV-ring theorem which gives a characterization of aV-ring. In this paper, we generalize this theorem toV-modules and consider some applications for Noetherian self-cogenerators.

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalized in convergence semigroups. In the discussion of maximal right simple subsemigroups and maximal right subgroups of semigroups, generalization of the results that no two maximal right simple subsemigroups and maximal right subgroups of a convergence semigroup intersect, is also established.

This paper deals with a generalization of Browder fixed point theorems and variational inequalities by relaxing the assumptions of compactness and continuity

Research on Wiener type spaces was initiated by N.Wiener in [15]. A number of authors worked on these spaces or some special cases of these spaces. A kind of generalization of the Wiener's definition was given by H.Feichtinger in [2] as a Banach spaces of functions (or measures, distributions) on locally compact groups that are defined by means of the global behaviour of certain local properties of their elements. In the present paper we discussed Wiener type spaces using the spacesAw,ωp,q(G)andFw,ωp,q(G)(c. f. [8]) as a local component, andLνr(G)as a global component, wherewandνare Beurling weights onGandωis a Beurling weight onGˆ(c. f. [13]).

In this paper, a generalization of a theorem of Mishra and Srivastava [4] on|C,1|ksummability factors has been proved.

In this paper we establish a continued fraction represetation for the ratioqftwo basic bilateral hypergeometric series2ψ2's which generalize Gauss' continued fraction for the ratio of two2F1's.

In this paper we give an embedding characterization ofθ-regularity using the Wallman-type compactlfication. The productivity ofθ-regularity and a slight generalization of Nagami's Product Theorem to non-Hausdorff paracompact∑-spaces we obtain as a corollary.

In 1973, Stieglitz [5] introduced a notion of FB-Convergence which provided a wide generalization of the classical idea of almost convergence due to Lorentz [1]. The concept of strong almost convergence was introduced by Maddox [3] who later on generalized this concept analogous to Stieglitz's extension of almost convergence [4]. In the present paper we define absolute FB-Convergence which naturally emerges from the concept of FB-Convergence.

A classTkof analytic functions in the unit disc is defined in which the concept of close-to-convexity is generalized. A necessary condition for a functionfto belong toTk, raduis of convexity problem and a coefficient result are solved in this paper.

This paper deals with a generalization of the Binary Quasi-Order Theorem. This generalization involves a more complicated algorithm than(0.2)t. Some remarks are made on relative merits of two dual algorithms called theψ-algorithm and theϕ-algorithm. Some illustrative examples are given.

The purpose of this paper is to show that for00are constants,0<ρ<1andθ(x)=∑p≤xlnp, wherepruns over the primes.

This paper is devoted to a generalization of the bifurcation theorem of Karsnosel'skii and Rabinowitz to the set valued situation.