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The paper deals with the application of concept mapping in teaching mathematics at the primary level of education (ISCED 1), as well as the experimental verification of its qualitative contribution to the process of education. The authors present results obtained in a sample survey aimed at monitoring possibilities of influencing pupils' relationship to teaching and mastery of mathematics using digital concept maps within the process of pedagogical intervention. The authors tested the degree to which digital concept maps influence changes in the pupils' opinions and attitudes to mathematics (subject popularity, interest in the subject, easiness of understanding, fear and apprehension of mathematics) while explaining and fixating the curriculum of selected mathematics topics in the third grade of a primary school. The results of the experiment did not confirm that teaching supported by concept maps contributes to reducing pupils' negative attitudes towards subjects, particularly in mathematics at the primary level (ISCED 1). Due to the pedagogical intervention of concept mapping, no statistically significant changes occurred in the pupils' attitudes to the observed factors of mathematics. However, the authors have come up with research findings that may be notable in the field of branch didactics of mathematics and digital technologies. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. [ABSTRACT FROM AUTHOR]

Abstract In 1995 Heath, Keppelmann and Wong studied a Nielsen type number N F (f , p) for a fibre preserving map f of fibration p. This number is a lower bound for the least number of fixed points within the fibre homotopy class of f. In this paper we generalize these ideas from fixed point theory to periodic point theory, and define two Nielsen type numbers N P n F (f , p) and N Φ n F (f , p) for periodic points of a fibre preserving map. These numbers, which can be thought of as the dual of periodic Nielsen type numbers for a relative map due to Heath, Schirmer and You, are bigger than the ordinary Nielsen type numbers. The definition of N P n F (f , p) and N Φ n F (f , p) is reminiscent of the naive type addition formulae for periodic points of fibre preserving maps due to Heath and Keppelmann. Some calculations and examples are given. [ABSTRACT FROM AUTHOR]

Based on the recent important result of S. S. Chang, H. W. Joseph Lee, C K. Chan, L. Wang, L.J. Qin [Appl. Math. Comput. 219 (2013) 10416-10424], we study in this article the split feasibility problem for a countable family of multi-valued k-strictly pseudo-contractive mappings and total asymptotically strict pseudo-contractive mappings in infinite dimensional Hilbert spaces. The main results presented in this paper improve and extend the aforementioned result. [ABSTRACT FROM AUTHOR]

In this paper a systematic study begins of the category b-UFIL of b-uniform filter spaces and b-uniformly continuous mappings. We will show that this construct forms a quasitopos in which quotients are stable under products. Consequently, it is extremely useful for further studies in the realm of Bounded topology. [ABSTRACT FROM AUTHOR]

In this paper we prove uniqueness theorems for mappings $F\in W_{\text{loc}}^{1,n}(\mathbb{B}^{n};\mathbb{R}^{n})$ of finite distortion $1\leq K(x)=\Vert \mathit{DF}(x)\Vert ^{n}/J_{F}(x)$ satisfying some integrability conditions. These types of theorems fundamentally state that if a mapping defined in $\mathbb{B}^{n}$ has the same boundary limit $a$ on a ‘relatively large’ set $E\subset \unicode[STIX]{x2202}\mathbb{B}^{n}$ , then the mapping is constant. Here the size of the set $E$ is measured in terms of its $p$ -capacity or equivalently its Hausdorff dimension. [ABSTRACT FROM AUTHOR]

In this paper we consider a simple algebraic structure — sets with a single endofunction. We shall see that from the point of view of structural limits, even this simplest case is both interesting and difficult. Nevertheless we obtain the shape of limit objects in the full generality, and we prove the inverse theorem in the case of quantifier-free limits. [ABSTRACT FROM AUTHOR]

Let ( T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote by ω( x, f) and P( f) the ω-limit set of x under f and the set of periodic points of f, respectively. Write Ω( x, f) = { y| there exist a sequence of points x ∈ T and a sequence of positive integers n < n < ··· such that lim x = x and lim $$f^{n_{k}}$$ ( x ) = y}. In this paper, we show that the following statements are equivalent: (1) f is equicontinuous. (2) ω( x, f) = Ω( x, f) for any x ∈ T. (3) ∩ f ( T) = P( f), and ω( x, f) is a periodic orbit for every x ∈ T and map h: x → ω( x, f) ( x ∈ T) is continuous. (4) Ω( x, f) is a periodic orbit for any x ∈ T. [ABSTRACT FROM AUTHOR]

The allowed patterns of a map are those permutations in the same relative order as the initial segments of orbits realized by the map. In this paper, we characterize and provide enumerative bounds for the allowed patterns of signed shifts, a family of maps on infinite words. [ABSTRACT FROM AUTHOR]

This paper investigates the structure of points u ∈ A N that are such that the omega-limit set ω ( u , σ ) is precisely X , where X ⊆ A N is an internally transitive shift space. We then use those results to study the possible structures of the omega-limit set of the turning point for a unimodal map. Examples are provided of unimodal maps f where no iterate of the turning point c is recurrent and ω ( c , f ) is either a minimal Cantor set or properly contains a minimal Cantor set. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Remling's theorem on canonical systems that the ω limit points of the Hamiltonian under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure of a canonical system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a concept of graph convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping in Banach spaces and prove an equivalence theorem between graph convergence and resolvent operator convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping. Further, we consider a system of generalized variational inclusions involving $$H(\cdot ,\cdot )$$ -co-accretive mapping in real $$q$$ -uniformly smooth Banach spaces. Using resolvent operator technique, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions under some suitable conditions. Further, we discuss the convergence of iterative algorithm using the concept of graph convergence. Our results can be viewed as a refinement and generalization of some known results in the literature. [ABSTRACT FROM AUTHOR]

The intent of this paper is to introduce the concept of Gb-cone metric and we describe some basic properties of such metric. Further, we establish some fixed point theorems for self-mappings satisfying the contractive type conditions and a common fixed theorem for two weakly compatible self-mappings satisfying the contractive condition in Gbcone metric spaces without the assumption of normality. Moreover, some examples are provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the further development of the theory of almost geodesic mappings of spaces with affine connection. [ABSTRACT FROM AUTHOR]

In this paper, by using the parametric representation of spirallike mappings, we construct to obtain the growth theorem of spirallike mappings on Reinhardt domain B. Moreover, the distortion theorem of spirallike mappings is obtained. [ABSTRACT FROM AUTHOR]

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish relationships between Lebesque and inductive dimensions ( m , n ) -dim and ( m , n ) -Ind. The main results are the following: 1. For every normal space X we have ( m , n ) - dim X = ⌊ dim X n ⌋ . 2. For every metrizable space X we have ( m , n ) - dim X = ( m , n ) - Ind X . [ABSTRACT FROM AUTHOR]

In this paper, we define and discuss the properties of Rω- and δω-sets in a topological space. We prove that the family of all Rω-sets is a base for the topology of all δω-sets. Also, we characterize codense of the ideal of all countable subsets by these sets. [ABSTRACT FROM AUTHOR]