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In [1] Kohli and Vashistha gave an analogue of probabilistic version of Pant's Theorem ([2], Theorem 1). We note that mappings defined in Examples 3.6 to 3.8 of [1] are not self maps as claimed in the Definitions 3.1 and 3.2. In this context, we provide some relevant examples to complete the interesting results. [ABSTRACT FROM AUTHOR]

The main results of the paper generalize the following classical theorem to the setting of line element D-manifolds: the automorphisms of a covariant derivative on a manifold are exactly the affinities that leave its torsion invariant. [ABSTRACT FROM AUTHOR]

This paper is a continuation of [7], where a duality theorem for the category HLC of locally compact Hausdorff spaces and continuous maps is proved. In the present paper, we characterize the injective and surjective morphisms of the category HLC, as well as of its cofull subcategories determined by the open, by the skeletal or by the perfect maps, by means of some corresponding properties of their dual morphisms. This is in analogy with some well-known results of M. H. Stone [17] and generalizes some similar results of de Vries [4]. Such characterizations are also obtained for the homeomorphic embeddings, dense embeddings, LCA-embeddings etc.; in particular a theorem of Fedorchuk [10, Theorem 6] is generalized. Again in analogy with some well-known results of M. H. Stone [17], the dual objects of the open, regular open, clopen, compact open, regular closed etc. subsets of a locally compact Hausdorff space X are directly described by means of the dual object of X; some of these results are new even in the compact case. An explicit description of the products of local contact algebras (= LC-algebras) in the category DHLC dual to the category HLC is given and a completion theory for LC-algebras is developed. [ABSTRACT FROM AUTHOR]

An open problem on orthogonality spaces posed by Jürg Rätz in [10] (also cf. [14] is completely solved in this paper, so that orthogonality spaces admitting nonzero even orthogonally additive mappings are completely described. As a by-product, a characterization of real inner product spaces is also given. [ABSTRACT FROM AUTHOR]

Let $${{\mathbb F}}$$ , $${{\mathbb K}}$$ be two fields of real or complex numbers and X, Y be two normed spaces over $${{\mathbb F}}$$ , $${{\mathbb K}}$$ , respectively. In this paper, we use a modification of Brzdęk's method in [] to obtain generalized hyperstability results for a general linear equation of the formwhere $${g \colon X \rightarrow Y}$$ is a mapping and $${a, b \in {\mathbb F}\backslash\{0\}}$$ , $${A, B \in \mathbb{K}}$$ . Our results are improvement and generalization of the main results of Piszczek []. [ABSTRACT FROM AUTHOR]

We prove Theorem 1.3 of [] under a more general situation and rectify some typographic errors that appear in the paper. [ABSTRACT FROM AUTHOR]

Let 1≦ m≦4 be a fixed integer and let f: X→ Y be a mapping with X, Y two vector spaces. The functional equation (1.1) is said to be additive if m=1, quadratic if m=2, cubic if m=3 and quartic if m=4, respectively. For convenience, a solution of (1.1) will be called an m-mapping. Let $\mathcal{A}$ , $\mathcal{B}$ be two algebras. An m-mapping $f\colon \mathcal{A} \to \mathcal{B}$ will be called m-derivation if the equality f( xy)= x f( y)+ f( x) y is fulfilled for all $x,y\in \mathcal{A}$ . In this paper, we use a fixed point method to prove the stability and hyperstability of m-derivations on Banach algebras. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some common fixed point theorems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples. [ABSTRACT FROM AUTHOR]

We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between s h,l ( λ, µ) = s((Δ − λ I) h) + s((Δ − µ I) l) and s γ. Among other things the aim of this paper is to reduce the set (s h,l( λ, µ), s γ to a set of the form S τ,γ. [ABSTRACT FROM AUTHOR]

Let ( E, ≦) be a vector lattice and E+ be the set of all nonnegative elements of E. We investigate M-functionals from E+ into ℝ+, that is functions A: E+ → ℝ+ such that for α ≧ 0 and f, g ɛ E+. Let X be a set and Σ be an algebra of subsets of X. By an M-measure we understand the function μ: Σ → ℝ+ such that μ( $$ \not 0 $$) = 0 and The main result of the paper is a Riesz type theorem. We prove that every M-functional on C( X, ℝ)+ can be expressed in terms of M-measure. [ABSTRACT FROM AUTHOR]

In [1], Açıkgöz et al. introduced and investigated the notions of w- I-continuous and w*- I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with continuous and θ-continuous functions. [ABSTRACT FROM AUTHOR]

Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ćirić and Rhoades and Watson. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study systems of strong implicit vector variational inequalities. Under suitable conditions, some existence results for systems of strong implicit vector variational inequalities are established by the Kakutani­Fan­Glicksberg fixed point theorem. [ABSTRACT FROM AUTHOR]

Let n be a positive integer. We characterize solutions f: X → ℝ of the equation f ( x + f( x) n y = f( x) f( y) mapping a real separable F-space X into ℝ, which are bounded on nonzero Christensen measurable sets. [ABSTRACT FROM AUTHOR]

We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between s h,l ( λ, µ) = s((Δ − λ I) h) + s((Δ − µ I) l) and s γ. Among other things the aim of this paper is to reduce the set (s h,l( λ, µ), s γ to a set of the form S τ,γ. [ABSTRACT FROM AUTHOR]

The main result of this paper is a fixed point theorem of self-mappings in Menger spaces which satisfy certain inequality. This inequality involves a class of real functions which we call Φ-functions. As a corollary we obtain a result in the corresponding metric spaces. The result is supported by an example. The class of real functions we have used is the conceptual extension of altering distance functions used in metric fixed point theory. [ABSTRACT FROM AUTHOR]

We introduce a new characterization of linear isometries. More precisely, we prove that if a one-to-one mapping f:ℝn→ℝn(2≦ n<∞) maps every regular pentagon of side length a> 0 onto a pentagon with side length b> 0, then there exists a linear isometry I :ℝn→ℝnup to translation such that f( x) = ( b/ a) I( x). [ABSTRACT FROM AUTHOR]

LetXbe a normed linear space and letSandTbe multi-valued mappings ofXinto a family of closed, not necessarily compact subsets ofX. In this paper some results on the convergence of the Ishikawa iterates associated with a pairS, Twhich satisfy the condition (8) below, are obtained. [ABSTRACT FROM AUTHOR]

Let T be a triangular algebra over a commutative ring R, ξ be an automorphism of T and Zξ(T) be the ξ-center of T. Suppose that q:T×T→T is an R-bilinear mapping and that Tq:T→T is a trace of q. The aim of this article is to describe the form of Tq satisfying the commuting condition [Tq(x),x]ξ=0 (resp. the centralizing condition [Tq(x),x]ξ∈Zξ(T)) for all x∈T. More precisely, we will consider the question of when Tq satisfying the previous condition has the so-called proper form. [ABSTRACT FROM AUTHOR]

The classical Lebedev index transform [3] involving squares and products of the Legendre functions is generalized on the associated Legendre functions of an arbitrary order. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. As an application, a solution to the boundary value problem for a third order partial differential equation is obtained. [ABSTRACT FROM AUTHOR]

We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps $${f : X\to Y}$$ of the class $${\alpha}$$ for wide classes of topological spaces. In particular, we prove that for a topological space X and a contractible space Y a map $${f : X \to Y}$$ belongs to the nth stable Baire class if and only if there exist a sequence $${(f_k)_{k=1}^\infty}$$ of continuous maps $${f_k : {X \to Y}}$$ and a sequence $${(F_k)_{k=1}^\infty}$$ of functionally ambiguous sets of the nth class in X such that $${f|_{F_k}=f_k|_{F_k}}$$ for every k. Moreover, we show that every monotone function $${f : \mathbb{R} \to \mathbb{R}}$$ is of the $${\alpha}$$ th stable Baire class if and only if it belongs to the first stable Baire class. [ABSTRACT FROM AUTHOR]

Let $${\mu}$$ be a probability measure with an infinite compact support on $${\mathbb{R}}$$ . Let us further assume that $${F_n:=f_n\circ\dots\circ f_1}$$ is a sequence of orthogonal polynomials for $${\mu}$$ where $${{(f_n)}_{n=1}^\infty}$$ is a sequence of nonlinear polynomials. We prove that if there is an $${s_0\in\mathbb{N}}$$ such that 0 is a root of f′ for each $${n > s_0}$$ then the distance between any two zeros of an orthogonal polynomial for $${\mu}$$ of a given degree greater than 1 has a lower bound in terms of the distance between the set of critical points and the set of zeros of some F. Using this, we find sharp bounds from below and above for the infimum of distances between the consecutive zeros of orthogonal polynomials for singular continuous measures. [ABSTRACT FROM AUTHOR]

We prove some stability results for the equation in the class of functions mapping a groupoid ( X, ∗) into a Banach space Y , where $${p, q, r, s: X \rightarrow X}$$ are endomorphisms of the groupoid, and A, B, C, D are fixed scalars. Particular cases of the equation are the equation of the p-Wright affine functions, the additive Cauchy equation, the Jensen equation, the quadratic equation and the general linear equation (in two variables). [ABSTRACT FROM AUTHOR]

We provide optimal values for m satisfying the partition relation $${{\forall l > 1, \alpha \rightarrow ({\rm top} \omega^{2} + 1)^{2}_{l,m}}}$$ when $${{\alpha = {\omega^{\omega}} +1}}$$ and when $${{\alpha = {\omega^{{\omega}^{k}}}, {\rm for every} k > 1}}$$ . [ABSTRACT FROM AUTHOR]

We completely classify λ-biharmonic slant surfaces and λ-biminimal Lagrangian surfaces in 2-dimensional complex space forms, under the condition that the mean curvature is nonzero constant. In addition, we provide some examples of λ-biminimal slant surfaces with nonzero constant mean curvature, which are neither Lagrangian nor λ-biharmonic. [ABSTRACT FROM AUTHOR]

For a map $${S : X \to X}$$ and an open connected set (= a hole) $${H \subset X}$$ we define $${\mathcal{J}_H(S)}$$ to be the set of points in X whose S-orbit avoids H. We say that a hole H is supercritical if The purpose of this note is to completely characterize all supercritical holes for the doubling map Tx = 2 x mod 1. [ABSTRACT FROM AUTHOR]

Let $${K,M,N : \mathbb{R}^{2} \rightarrow \mathbb{R}}$$ be translative functions. Then K is invariant with respect to the mapping $${(M,N) : \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}}$$ if and only if the functions $${h = K(\cdot, 0), f = M(\cdot, 0), g = N(\cdot, 0)}$$ satisfy the functional equation If K, M, N are means, then h(0) = f(0) = g(0) = 0. The formal power solutions and analytic solutions of this functional equation, satisfying these initial conditions, are considered. [ABSTRACT FROM AUTHOR]

Let ( X, d) and ( Y, d) be semimetric spaces with distance sets D( X) and D( Y), respectively. A mapping F: X→ Y is a weak similarity if it is surjective and there exists a strictly increasing f: D( Y)→ D( X) such that d= f∘ d∘( F⊗ F). It is shown that the weak similarities between geodesic spaces are usual similarities and every weak similarity F: X→ Y is an isometry if X and Y are ultrametric and compact with D( X)= D( Y). Some conditions under which the weak similarities are homeomorphisms or uniform equivalences are also found. [ABSTRACT FROM AUTHOR]

We give a description of those functions f in the unit ball [InlineEquation not available: see fulltext.] of H on the disk $\mathbb{D}$ whose orbit { f∘ ϕ: n∈ℕ} is locally uniformly dense in [InlineEquation not available: see fulltext.] for some sequence ( ϕ) of selfmaps of $\mathbb{D}$. An interpretation of this result in terms of the superposition (or substitution) operator on the space [InlineEquation not available: see fulltext.] of holomorphic selfmaps of $\mathbb{D}$ is given, too. Finally we present a new class of functions in H whose orbit in H under the hyperbolic composition operator is non-minimal. [ABSTRACT FROM AUTHOR]

The connection between transitivity and existence of a dense orbit for multifunctions $\phi \: X\multimap X$ in generalized topological spaces is studied. Moreover strongly transitive multifunctions and functions in generalized topological spaces are investigated. [ABSTRACT FROM AUTHOR]

Extremal disconnectedness is further investigated for generalized topological spaces. It is found that extremally disconnected generalized topological spaces are a rich source of generalized lower semi-continuous and generalized upper semi-continuous mappings. [ABSTRACT FROM AUTHOR]

Let S be a foundation locally compact topological semigroup, and let M( S) be the space of all measures μ∈ M( S) for which the maps x↦| μ|∗ δ and x↦| μ|∗ δ from S into M( S) are weakly continuous. The purpose of this article is to develop a notion of character amenability for semigroup algebras. The main results concern the χ-amenability of M( S). We give necessary and sufficient conditions for the existence of a left χ-mean on M( S). [ABSTRACT FROM AUTHOR]

We give a systematic discussion on the relationship among generalized topologies, generalized neighborhood systems, and generalized interior operators. As some applications, we answer a question raised in [7] by Shen, and characterize generalized continuous maps. [ABSTRACT FROM AUTHOR]

definition of a generalized quotient topology is given and some characterizations of this concept, up to generalized homeomorphisms, are furnished. For the first approach, we exhibit a monotonic map spanning that generalized quotient topology. We also prove that the notions of generalized normality and generalized compactness are preserved by those quotient structures. [ABSTRACT FROM AUTHOR]

Without any regularity conditions, we determine all the Cauchy means C that are invariant with respect to the mean-type mapping ( L, L) where L denotes the Lagrangean mean generated by f. Applications in iteration theory and functional equation are given. [ABSTRACT FROM AUTHOR]

classical insertion theorem due to Katětov-Tong (or Dowker-Katětov, Michael) reads that ℝ can be a test space for the range of maps on the insertion theorem which characterizes the domain to be normal (or normal and countably paracompact, perfectly normal). It is known that the range ℝ in the Katětov-Tong insertion theorem is not necessarily replaced by a non-trivial separable Banach lattice. We show that the range ℝ in the Dowker-Katětov and Michael insertion theorems can be replaced by any non-trivial separable Banach lattice. [ABSTRACT FROM AUTHOR]

We investigate g-functions based on semigroups related to multi-dimensional Laguerre function expansions of convolution type. We prove that these operators can be viewed as Calderón-Zygmund operators in the sense of the underlying space of homogeneous type, hence their mapping properties follow from the general theory. [ABSTRACT FROM AUTHOR]

Generalizing de Vries' duality theorem [9], we prove that the category HLC of locally compact Hausdorff spaces and continuous maps is dual to the category DHLC of complete local contact algebras and appropriate morphisms between them. [ABSTRACT FROM AUTHOR]

We prove new common fixed point theorems for weakly compatible mappings on uniform spaces. Also, an application to locally convex spaces is presented. [ABSTRACT FROM AUTHOR]

We obtain two countable properties of spaces with a point-countable sn-network, establish the mapping relation between spaces with a point-countable wcs*-network of certain property and locally separable metric spaces, and partially correct a gap in [8]. [ABSTRACT FROM AUTHOR]

A sufficient condition for the strict insertion of a continuous function between two comparable upper and lower semicontinuous functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker. Our insertion lemma also provides purely topological proofs of some standard results on closed subsets of normal spaces which normally depend upon uniform convergence of series of continuous functions. We also establish a Tietze-type extension theorem characterizing closed G δ -sets in a normal space. [ABSTRACT FROM AUTHOR]

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. [ABSTRACT FROM AUTHOR]

We give a Pontryagin-Thom type construction for Stein factorizations of fold maps of 3-manifolds into the plane. As an application, we compute the cobordism group of Stein factorizations of fold maps of oriented 3-manifolds into the plane and the oriented cobordism group of fold maps of 3-manifolds into the plane. It turns out that these two groups are isomorphic to Z 2 ⊕ Z 2. We have the analogous results about bordism groups as well. [ABSTRACT FROM AUTHOR]

We show that, under some weak regularity conditions, an approximately microperiodic function, mapping a semitopological group into the set of reals, is close to a constant function. [ABSTRACT FROM AUTHOR]

We investigate the interrelations of some families of weak forms of open sets and point out that some of them are the same. Also, we make comparisons of some weak forms of continuity and give decompositions of some of them. [ABSTRACT FROM AUTHOR]

A new class of sets called π gs-closed sets is introduced and its properties are studied. Moreover the notions of π gs- T 1/2 spaces and π gs-continuity are introduced. [ABSTRACT FROM AUTHOR]

Amini-Harandi proved that alternate convexically nonexpansive mappings on non-empty weakly compact convex subsets of strictly convex Banach spaces have fixed points. We prove that Amini-Harandi's result holds also in Banach spaces with the Kadec--Klee property and the result is true for a larger class of mappings. Moreover, we show that the Alspach mapping in L 1[0,1] is not a 2-alternate convexically nonexpansive mapping. [ABSTRACT FROM AUTHOR]

The following two theorems are obtained. (1) A mapping fis A-continuous if and only if it is semi-continuous and C-continuous. (2) A mapping f is A-continuous if and only if it is spr-continuous and LC-continuous. [ABSTRACT FROM AUTHOR]

Let Abe a semisimple H*-algebra and let T: A→ A be an additive mapping such that 2T( x n +1)= T( x) x n+ x n T( x) holds for all x∈ A and some integer n≧1. In this case T is a left and a right centralizer. [ABSTRACT FROM AUTHOR]

Let f: X→ Y be a mapping. f is called a sequence-covering mapping if in case S is a convergent sequence containing its limit point in Y then there is a compact subset K of X such that f( K) = S. It is shown that each quotient and compact mapping of a metric space is sequence-covering. [ABSTRACT FROM AUTHOR]