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Abstract: Huang and Zhang reviewed cone metric spaces in 2007 [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476]. We shall prove that there are no normal cones with normal constant and for each there are cones with normal constant . Also, by providing non-normal cones and omitting the assumption of normality in some results of [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476], we obtain generalizations of the results. [Copyright &y& Elsevier]

In an important paper [24] , Reimann showed that the flow mappings of a continuous vector field of Zygmund class Λ ⁎ are quasisymmetric homeomorphisms. In this paper, we will discuss the flow mappings when the vector field belongs to the smooth Zygmund class λ ⁎ or the Sobolev class H 3 2 . [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of geodesic mappings and infinitesimal geodesic deformations of generalized Riemannian spaces. While a geodesic mapping between two generalized Riemannian spaces any geodesic line of one space sends to a geodesic line of the other space, under an infinitesimal geodesic deformation any geodesic line is mapped to a curve approximating a geodesic with a given precision. Basic equations of the theory of geodesic mappings in the case of generalized Riemannian spaces are obtained in this paper. A new generalization of the famous Levi Civita's equation is found. Necessary and sufficient conditions for a nontrivial infinitesimal geodesic deformation are given. It is proven that a generalized Riemannian space admits nontrivial infinitesimal geodesic deformations if and only if it admits nontrivial geodesic mappings. At last it is shown that generalized equidistant spaces of primary type admit nontrivial geodesic deformations. [ABSTRACT FROM AUTHOR]

A subset E of an infinitely dimensional linearly-topological space X is called spaceable if there is an infinitely dimensional closed subspace Y of X with Y ⊂ E ∪ { 0 } . The main aim of the paper is to show the spaceability of the following sets: 1. the set of those ( f , g ) ∈ L p × L q for which f g ∉ L r provided that one of the following conditions holds: (a) 0 < 1 p + 1 q < 1 r and sup ⁡ { μ ( A ) : μ ( A ) < ∞ } = ∞ ; (b) 1 p + 1 q > 1 r and inf ⁡ { μ ( A ) : μ ( A ) > 0 } = 0 ; 2. the set of those ( f , g ) ∈ C 0 × C 0 for which fg is not integrable, where C 0 is the space of continuous mappings which vanish at infinity; 3. the set of those ( f , g ) ∈ L p ( G ) × L q ( G ) for which the convolution f ⋆ g is not well-defined or is equal to ∞ provided G is a locally compact but non-compact topological group and p , q > 1 with 1 / p + 1 / q < 1 . The paper can be considered as a continuation of our previous ones in which we studied these sets from the Baire category and σ -porosity points of view. [ABSTRACT FROM AUTHOR]

Abstract An operator T on a complex Hilbert space H is said to be complex symmetric if there exists a conjugate-linear, isometric involution C : H → H so that C T C = T ⁎. This paper is devoted to describing which linear maps leave the class of complex symmetric operators invariant. Complete characterizations are obtained for several classes of linear maps, including similarity transformations, surjective linear isometries, multiplication operators and certain completely positive maps. [ABSTRACT FROM AUTHOR]

Abstract The purpose of this paper is to investigate a parabolic problem with coupled reaction terms and free boundary, including the existence, uniqueness, regularity and long-time behavior of positive solutions. Firstly, by the contraction mapping theorem, we establish the (local) existence and uniqueness of positive solutions. Then, we prove the solution blows up in finite time with large initial data by comparison principle, and give more details for these large initial data by exhibiting an energy condition. The simultaneous blow-up result of the maximum of u and v is obtained, and the blow-up set of blow-up solutions is a compact subset of [ 0 , h 0 ]. Furthermore, there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small, while there is a global and slow solution provided that the initial datum is suitably large. Finally, for initial data σ (φ (x) , ψ (x)) , we obtain a trichotomy conclusion by considering the size of parameter σ. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the general solution of the following general radical quintic functional equation f ( a x 5 + b y 5 5 ) = r f ( x ) + s f ( y ) for f a mapping from the field of real numbers into a vector space, where a , b , r , s are fixed nonzero reals. Also, we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem (cf. Dung and Hang (2018) [15] , Theorem 2.1) in quasi- β -Banach spaces. Namely, we show, under some weak natural assumptions, functions satisfying the above equation approximately (in some sense) must be actually solutions to it. [ABSTRACT FROM AUTHOR]

For a tangential slit, the behavior of the driving function in the Loewner differential equation is less clear. In this paper, we investigate the tangential slit φ ( Γ ) , where φ is a univalent real analytic function near the origin, and where Γ is a circular arc tangent at the origin. Our main aim is to give an interesting way to prove the asymptotic property of the driving function which generates the tangential slit φ ( Γ ) . [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of hyperbolic harmonic mappings in the unit ball B n in R n ( n ≥ 2 ) . Firstly, we establish necessary and sufficient conditions for a hyperbolic harmonic mapping to be in the Bloch space B ( B n ) and the generalized Bloch space L ∞ , ω B α , a 0 ( B n ) , respectively. Secondly, we discuss the relationship between the integral means of hyperbolic harmonic mappings and that of their gradients. The obtained results are the generalizations of Hardy and Littlewood's related ones in the setting of hyperbolic harmonic mappings. Finally, we characterize the weak uniform boundedness property of hyperbolic harmonic mappings in terms of the quasihyperbolic metric. [ABSTRACT FROM AUTHOR]

Let a data set Δ = { ( t i , y i ) ∈ R × Y : i = 0 , 1 , ⋯ , N } be given, where t 0 < t 1 < t 2 < ⋯ < t N and Y is a complete metric space. In this article, fractal interpolation functions (FIFs) on I = [ t 0 , t N ] corresponding to the set Δ are constructed by mappings W 1 , ⋯ , W N . Each W k is of the form W k = ( L k , M k ) , where L k : J k → I k is a homeomorphism and M k : J k × Y → Y is continuous. Here I k = [ t k − 1 , t k ] and J k = [ t j ( k ) , t l ( k ) ] , j ( k ) , l ( k ) ∈ { 0 , 1 , ⋯ , N } , are subintervals of I which depend on k . In this construction, the length of J k is not assumed to be larger than the length of I k , and each L k is not supposed to be a contraction. A FIF established by this method has a property of self similarity between its graph on J k and on I k . In this paper we give a construction of FIFs with locally self similar graphs. The stability and sensitivity of FIFs established in this way are also discussed. [ABSTRACT FROM AUTHOR]

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book [2] by Baird and Wood for details). In this paper, we study generalized harmonic morphisms which are defined to be maps between Riemannian manifolds that pull back harmonic functions to biharmonic functions. We obtain some characterizations of generalized harmonic morphisms into a Euclidean space and give two methods of constructions that can be used to produce many examples of generalized harmonic morphisms which are not harmonic morphisms. We also give a complete classification of generalized harmonic morphisms among the projections of a warped product space, which provides infinitely many examples of proper biharmonic Riemannian submersions and conformal submersions from a warped product manifold. [ABSTRACT FROM AUTHOR]

In this paper, the third in our sequence of papers on multivariate stochastic mappings, we focus on the type of, not necessarily stationary, stochastic mappings that are representable with the aid of a certain operator semigroup, called module propagator. As in the previous papers we obtain neater results for multivariate second order random distribution fields, from which the main result regards the extension to this setting of the theory of uniformly bounded linearly stationary random fields. [ABSTRACT FROM AUTHOR]

In this paper we study integral estimates of derivatives of conformal mappings φ : D → Ω of the unit disc D ⊂ C onto bounded domains Ω that satisfy the Ahlfors condition. These integral estimates lead to estimates of constants in Sobolev–Poincaré inequalities, and by the Rayleigh quotient we obtain spectral estimates of the Neumann–Laplace operator in non-Lipschitz domains (quasidiscs) in terms of the (quasi)conformal geometry of the domains. Specifically, the lower estimates of the first non-trivial eigenvalues of the Neumann–Laplace operator in some fractal type domains (snowflakes) were obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study common fixed point properties for a family of mappings. We present the extensions of Caristi's fixed point theorem and Markov–Kakutani fixed point theorem for a family of set-valued mappings. [ABSTRACT FROM AUTHOR]

This paper considers a class of delayed reaction–diffusion systems under the Neumann boundary condition which arise in epidemiology and can describe the temporal and spatial evolutionary phenomena for the bacteria population and the human infective population. With the help of the iterative properties of interval mapping and dynamical system approaches, some positively invariant sets and attractive basins of the considered systems are analyzed detailedly. In addition, combining the global attractivity of interval mapping, we provide some sufficient conditions to ensure local or global attractivity of steady states of the systems. Finally, we apply these theoretical results to some models with different nonlinearity demonstrating “force of infection”, and then obtain some sufficient conditions about “force of infection” to describe the survival and extinction of bacteria and infective populations. [ABSTRACT FROM AUTHOR]

In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's bilinear estimates, and the results may be regarded as an extension of [8,21] to Stokes systems. [ABSTRACT FROM AUTHOR]

Iterative roots of mappings are of special interests because it defines fractional iteration, displays middle procedure of evolution and proposes a weak version of the embedding flow problem. For PM functions of height 1, the class of 1-dimensional mappings having the simplest nonmonotonicity, the existence of continuous iterative roots of any order was obtained under the characteristic endpoints condition and the condition was proved to be necessary for those orders greater than the number of forts plus 1. This suggests an open question about iterative roots without that condition, called the question on characteristic endpoints. In this paper, the question is answered completely in the case that the number of forts is equal to the order. Although results of nonexistence are also obtained for the case that the number of forts is greater than the order, a full description is still open. [ABSTRACT FROM AUTHOR]

Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various (equivalent) definitions for more than two decades, it has attracted much less attention than its older “siblings”, the metric regularity and the strong (metric) regularity. The purpose of this paper is to show that the strong metric subregularity shares the main features of these two most popular regularity properties and is not less instrumental in applications. We show that the strong metric subregularity of a mapping F acting between metric spaces is stable under perturbations of the form f + F , where f is a function with a small calmness constant. This result is parallel to the Lyusternik–Graves theorem for metric regularity and to the Robinson theorem for strong regularity, where the perturbations are represented by a function f with a small Lipschitz constant. Then we study perturbation stability of the same kind for mappings acting between Banach spaces, where f is not necessarily differentiable but admits a set-valued derivative-like approximation. Strong metric q -subregularity is also considered, where q is a positive real constant appearing as exponent in the definition. Rockafellar's criterion for strong metric subregularity involving injectivity of the graphical derivative is extended to mappings acting in infinite-dimensional spaces. A sufficient condition for strong metric subregularity is established in terms of surjectivity of the Fréchet coderivative, and it is shown by a counterexample that surjectivity of the limiting coderivative is not a sufficient condition for this property, in general. Then various versions of Newton's method for solving generalized equations are considered including inexact and semismooth methods, for which superlinear convergence is shown under strong metric subregularity. As applications to optimization, a characterization of the strong metric subregularity of the KKT mapping is obtained, as well as a radius theorem for the optimality mapping of a nonlinear programming problem. Finally, an error estimate is derived for a discrete approximation in optimal control under strong metric subregularity of the mapping involved in the Pontryagin principle. [ABSTRACT FROM AUTHOR]

In this paper we introduce the class of the inner p -quasiconformal mappings, that are homeomorphisms f : D ⟶ o n t o D , f ∈ W loc 1 , 1 ( D ; D ) , where D ⊂ R 2 is the unit disk, such that there exists a constant K p ≥ 0 for which the following distortion inequality | D f ( x ) | p ≤ K p | J f ( x ) | p − 1 a.e. x ∈ D is satisfied. The study of such mappings is motivated by the fact that their inverses satisfy the distortion inequality introduced in [11] . Here we give a characterization of them so that their components solve a suitable uniformly elliptic p -harmonic system. Moreover, for mappings satisfying the previous distortion inequality with K p = K p , f ( x ) not necessarily constant, we identify the homeomorphism f whose p -distortion function K p , f ( x ) is minimal in L 1 norm. [ABSTRACT FROM AUTHOR]

It is unknown if there exists a locally α -Hölder homeomorphism f : R 3 → H 1 for any 1 2 < α ≤ 2 3 , although the identity map R 3 → H 1 is locally 1 2 -Hölder. More generally, Gromov asked: Given k and a Carnot group G , for which α does there exist a locally α -Hölder homeomorphism f : R k → G ? Here, we equip a Carnot group G with the Carnot–Carathéodory metric. In 2014, Balogh, Hajłasz, and Wildrick considered a variant of this problem. These authors proved that if k > n , there does not exist an injective, ( 1 2 + ) -Hölder mapping f : R k → H n that is also locally Lipschitz as a mapping into R 2 n + 1 . For their proof, they use the fact that H n is purely k -unrectifiable for k > n . In this paper, we will extend their result from the Heisenberg group to model filiform groups and Carnot groups of step at most three. We will now require that the Carnot group is purely k -unrectifiable. The main key to our proof will be showing that ( 1 2 + ) -Hölder maps f : R k → G that are locally Lipschitz into Euclidean space, are weakly contact. Proving weak contactness in these two settings requires understanding the relationship between the algebraic and metric structures of the Carnot group. We will use coordinates of the first and second kind for Carnot groups. [ABSTRACT FROM AUTHOR]

In this paper we consider support points for the family S g 0 ( B 2 ) of mappings with g -parametric representation on the Euclidean unit ball B 2 in C 2 , where g is a univalent function on the unit disc U in C , which satisfies certain natural assumptions. We shall use the shearing process recently introduced by Bracci, to prove the existence of bounded support points for the family S g 0 ( B 2 ) . This result is in contrast to the one dimensional case, where all support points of the family S are unbounded. We also study the case of time- log ⁡ M reachable families R ˜ log ⁡ M ( id B 2 , M g ) generated by the Carathéodory family M g , and obtain certain results and applications, which show a basic difference between the theory in the case of one complex variable and that in higher dimensions. Of particular interest is the case where g is a convex (univalent) function on U . Finally, various consequences and certain conjectures are also considered. [ABSTRACT FROM AUTHOR]

In this paper we study the structure, weak continuity and approximability properties for the integer multiplicity rectifiable currents carried by the graphs of maximal semi-monotone set-valued maps on an n -dimensional convex domain. Especially, we give an enhanced version of approximation theorem for the subgradients of semi-convex functions. [ABSTRACT FROM AUTHOR]

A 2 p -times continuously differentiable complex valued function f = u + i v in a simply connected domain Ω is polyharmonic (or p-harmonic ) if it satisfies the polyharmonic equation △ p F = 0 . Every polyharmonic mapping f can be written as f ( z ) = ∑ k = 1 p | z | 2 ( p − 1 ) G p − k + 1 ( z ) , where each G p − k + 1 is harmonic. In this paper we investigate the univalence of polyharmonic mappings on linearly connected domains and the relation between univalence of f ( z ) and that of G p ( z ) . The notion of stable univalence and logpolyharminc mappings are also considered. [ABSTRACT FROM AUTHOR]

In this article, we establish a truncated non-integrated defect relation for meromorphic mappings from an m -dimensional complete Kähler manifold into P n ( C ) intersecting q hypersurfaces Q 1 , . . . , Q q in k -subgeneral position of degree d i , i.e., the intersection of any k + 1 hypersurfaces is emptyset. We will prove that ∑ i = 1 q δ f [ u − 1 ] ( Q i ) ≤ ( k − n + 1 ) ( n + 1 ) + ϵ + ρ u ( u − 1 ) d , where u is explicitly estimated and d is the least common multiple of d i ′ s. Our result generalizes and improves previous results. In the last part of this paper we will apply this result to study the distribution of the Gauss map of minimal surfaces. [ABSTRACT FROM AUTHOR]

In the present paper we study geodesic mappings between generalized Riemannian GR N and generalized Kählerian spaces of the third type G K 3 N , and specially the case when these spaces have the same torsions at corresponding points. Using the non-symmetric metric tensor we find necessary and sufficient conditions for the existence of geodesic mapping f : GR N → G K 3 ‾ N with respect to the four kinds of covariant derivatives. [ABSTRACT FROM AUTHOR]

In this paper we prove the admissibility of modular function spaces E ρ considered and defined by Kozłowski in [17] . As an application we get that any compact and continuous mapping T : E ρ → E ρ has a fixed point. Moreover, we prove that the same holds true for any retract of E ρ . [ABSTRACT FROM AUTHOR]

In this short paper we consider the connections between the specification property introduced by Bowen and ω -chaos introduced by Li. We show that if f : X → X is a continuous surjection of a compact metric space with the specification property and uniform expansion near a fixed point then the system ( X , f ) is ω -chaotic. [ABSTRACT FROM AUTHOR]

In this paper we consider a system with nonlocal dispersal. Applying Ahmad and Lazers definitions of lower and upper averages of a function and using the sub- and supersolution methods for PDEs we give sufficient conditions for permanence in such models. Moreover, we allow the intrinsic growth rates to be negative. [ABSTRACT FROM AUTHOR]

In this paper, we study α ¯ -harmonic mappings with an integer exponent and obtain a representation theorem which determines the relation between α ¯ -harmonic mappings and Euclidean harmonic mappings. As two applications of this representation theorem, we obtain a counterexample of the Radó–Kneser–Choquet theorem for α ¯ -harmonic mappings and show that the Lipschitz continuity of an α ¯ -harmonic mapping with an integer exponent is determined by the Euclidean harmonic mapping with same boundary. [ABSTRACT FROM AUTHOR]

In this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space ℓ 1 . Nominally, our result involves nonexpansive mappings, uniformly Lipschitzian mappings and cascading nonexpansive mappings. We also extend the results to some more general classes of Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we first construct a type of Möbius transformations with Clifford coefficients and give some of its properties, for example: the mapping properties, preserving the symmetric points with respect to the sphere, the Jacobi determinant, the monogenic properties under these Möbius transformations. Then by using the integral representation formulas for harmonic functions with values in a Clifford algebra C (Vn, 0) and the integral inequality estimation, we give the Schwarz lemma for harmonic functions with values in a Clifford algebra C (Vn, 0), which is sharper than the known results. Combining the Schwarz lemma with the Möbius transformations, the Schwarz-Pick type lemmas for functions with values in C (Vn, 0) are given. These results greatly improve the results in [21]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems (Helton et al. (2009) , de Oliviera et al. (2009) ). In the earlier paper (Helton et al. (2009) ) we characterized NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the boundary to the boundary; such maps we call “NC ball maps”. In this paper we turn to a more general dimension-free ball , called a “pencil ball”, associated with a homogeneous linear pencil For , define and let We study the generalization of NC ball maps to these pencil balls , and call them “pencil ball maps”. We show that every has a minimal dimensional (in a certain sense) defining pencil . Up to normalization, a pencil ball map is the direct sum of with an NC analytic map of the pencil ball into the ball. That is, pencil ball maps are simple, in contrast to the classical result of D''Angelo (1993) showing there is a great variety of such analytic maps from to when . To prove our main theorem, this paper uses the results of our previous paper (Helton et al. (2009) ) plus entirely different techniques, namely, those of completely contractive maps. What we do here is a small piece of the bigger puzzle of understanding how Linear Matrix Inequalities (LMIs) behave with respect to noncommutative change of variables. [Copyright &y& Elsevier]

Abstract: In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers–Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers–Ulam stability for general additive functional equations in quasi-β-normed spaces. [Copyright &y& Elsevier]

Abstract: In a Polish group G, a property is said to hold for a generic if the set on which it does not hold is meager in G; a property holds for almost every (ae) if the set on which it does not hold is Haar null. In this paper we study the properties of generic and ae elements of the Baer–Specker Group , the space of all self-maps of . We find that with respect to most of the properties under consideration in this paper, the properties of a generic element and ae element are complementary. Our results are similar in flavor to results by Dougherty and Mycielski for the group of all permutations of . [Copyright &y& Elsevier]

Abstract: We consider the general variational inequality , where F and g are mappings from a Hilbert space into itself and C is intersection of the fixed point sets of a finite family of nonexpansive mappings. We suggest and analyze an iterative algorithm with variable parameters as follows: The sequence is shown to converge in norm to the solutions of the general variational inequality under some mild conditions. Application to constrained generalized pseudo-inverse is included. Since the general variational inequalities include variational inequalities, quasi-variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]

Abstract: Let be a commutative family of nonexpansive mappings of a closed convex subset C of a reflexive Banach space X such that the set of common fixed point is nonempty. In this paper, we suggest and analyze a new viscosity iterative method for a commutative family of nonexpansive mappings. We also prove that the approximate solution obtained by the proposed method converges to a solution of a variational inequality. Our method of proof is simple and different from the other methods. Results proved in this paper may be viewed as an improvement and refinement of the previously known results. [Copyright &y& Elsevier]

Abstract: Motivated by the accomplishment of the second main theorem with moving targets, many authors studied the moving target problems in value distribution theory and related topics. In this paper, we prove some big Picard''s theorems for holomorphic mappings of several complex variables into with moving hyperplanes, related to Nochka''s little Picard-type theorems. As its application, we give a new quasi-normal criterion for families of meromorphic mappings of several complex variables into with moving hyperplanes. The new results in this paper greatly improve some earlier related results. [Copyright &y& Elsevier]

Abstract: Recently, Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435–447] introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi-contractive mappings and showed the stability of these iterative procedures with errors in Banach spaces. In this paper, we introduce a new concept of a couple of q-contractive-like mappings () in a Banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q-contractive-like mappings. The results established in this paper improve, extend and unify the corresponding ones of Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435–447], Chidume [C.E. Chidume, Approximation of fixed points of quasi-contractive mappings in spaces, Indian J. Pure Appl. Math. 22 (1991) 273–386], Chidume and Osilike [C.E. Chidume, M.O. Osilike, Fixed points iterations for quasi-contractive maps in uniformly smooth Banach spaces, Bull. Korean Math. Soc. 30 (1993) 201–212], Liu [Q.H. Liu, On Naimpally and Singh''s open questions, J. Math. Anal. Appl. 124 (1987) 157–164; Q.H. Liu, A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings, J. Math. Anal. Appl. 146 (1990) 301–305], Osilike [M.O. Osilike, A stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math. 27 (1996) 25–34; M.O. Osilike, Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math. 28 (1997) 1251–1265] and many others in the literature. [Copyright &y& Elsevier]

Abstract: In a recent paper we provided a characterization of triangular maps of the square, i.e., maps given by , satisfying condition (P1) that any chain recurrent point is periodic. For continuous maps of the interval, there is a list of 18 other conditions equivalent to (P1), including (P2) that there is no infinite ω-limit set, (P3) that the set of periodic points is closed and (P4) that any regularly recurrent point is periodic, for instance. We provide an almost complete classification among these conditions for triangular maps, improve a result given by C. Arteaga [C. Arteaga, Smooth triangular maps of the square with closed set of periodic points, J. Math. Anal. Appl. 196 (1995) 987–997] and state an open problem concerning minimal sets of the triangular maps. The paper solves partially a problem formulated by A.N. Sharkovsky in the eighties. The mentioned open problem, the validity of (P4) ⇒ (P3), is related to the question whether some regularly recurrent point lies in the fibres over an f-minimal set possessing a regularly recurrent point. We answered this question in the positive for triangular maps with nondecreasing fiber maps. Consequently, the classification is completed for monotone triangular maps. [Copyright &y& Elsevier]

Abstract: In this paper, weak and strong convergence theorems of the modified Noor iterations with errors are established for asymptotically nonexpansive mappings in Banach spaces. The results obtained in this paper extend and improve the several recent results in this area. [Copyright &y& Elsevier]

Abstract: In this paper, weak and strong convergence theorems are established for a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by the new iterative scheme. The results obtained in this paper extend and improve the recent ones announced by Xu and Noor, Glowinski and Le Tallec, Noor, Ishikawa, and many others. [Copyright &y& Elsevier]

Abstract: This paper considers Gibbs'' phenomenon for scaling vectors in . We first show that a wide class of multiresolution analyses suffer from Gibbs'' phenomenon. To deal with this problem, in [Contemp. Math. 216 (1998) 63–79], Walter and Shen use an Abel summation technique to construct a positive scaling function , , from an orthonormal scaling function φ that generates . A reproducing kernel can in turn be constructed using . This kernel is also positive, has unit integral, and approximations utilizing it display no Gibbs'' phenomenon. These results were extended to scaling vectors and multiwavelets in [Proceedings of Wavelet Analysis and Multiresolution Methods, 2000, pp. 317–339]. In both cases, orthogonality and compact support were lost in the construction process. In this paper we modify the approach given in [Proceedings of Wavelet Analysis and Multiresolution Methods, 2000, pp. 317–339] to construct compactly supported positive scaling vectors. While the mapping into associated with this new positive scaling vector is not a projection, the scaling vector does produce a Riesz basis for and we conclude the paper by illustrating that expansions of functions via positive scaling vectors exhibit no Gibbs'' phenomenon. [Copyright &y& Elsevier]

In this paper we extend and simplify the main result of [4] . [ABSTRACT FROM AUTHOR]

Let K be a hypergroup with a Haar measure. This paper consists of two themes; fixed point properties for non-expansive and affine maps. The first theme provides a condition when a non-expansive self-map on a weak (weak ⁎ ) compact convex subset of several function spaces over K has a fixed point while the second theme presents some applications of common fixed point properties for affine actions of K . [ABSTRACT FROM AUTHOR]

In the present paper we will use the inverse polynomial image method in order to construct optimal nodes of interpolation on unions of disjoint intervals. We will show how this method works on those disjoint intervals which possess so-called T-polynomials, and also prove that the method becomes ineffective in the absence of T-polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the relationship between the coarsely quasihyperbolic mappings and the quasisymmetric mappings, and show that a homeomorphism is a coarsely quasihyperbolic mapping which implies that it is quasisymmetric in the quasihyperbolic metric between two suitable metric spaces. [ABSTRACT FROM AUTHOR]

This paper studies the equivalence of the quasisymmetric mappings on non-connected sets. We introduce a generalized form of weak quasisymmetry and prove that, on a uniformly perfect metric space, a generalized weakly quasisymmetric mapping is quasisymmetric. We further improve this result on Cantor-like sets satisfying the small gap condition. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a coincidence point theorem for sequentially weakly continuous maps. Moreover, as a consequence, a critical point theorem for functionals possibly containing a nonsmooth part is obtained. Finally, as an application, existence results for nonlinear differential problems depending also on the derivative of the solution are established. [ABSTRACT FROM AUTHOR]

In the present paper we study equitorsion geodesic mappings between two generalized Riemannian spaces f : GR N → G R ‾ N . In this case these spaces have the same torsions at corresponding points. We prove that a generalized Riemannian space GR N admits an equitorsion geodesic mapping onto a generalized Riemannian space G R ‾ N if and only if in GR N certain differential equations of Cauchy type in covariant derivatives of the θ = 1 , … , 4 kinds have a solution with respect to the unknown tensor a i j , the gradient vector λ i ≠ 0 , and the differentiable function μ θ , θ = 1 , … , 4 . In fact we find four systems of PDE all equivalent to the existence of an equitorsion geodesic mapping and discuss the number of linearly independent solutions of this system of PDE. We establish an upper bound for the number of solutions for the geometrical problem under consideration. [ABSTRACT FROM AUTHOR]

In this paper we prove that a generalization of complex Π-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism. [ABSTRACT FROM AUTHOR]