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1
Content available On monotonicity of real functions
EN
Monotonicity of functions were of great interest of many mathematicians. Starting from the well known theorem of monotonicity of a differentiable function one can get quite sophisticated results. We give a survey of results when thesis of them is continuous and monotone function. Someone can ask why it should be continuous. Even a differentiable functions but not at the only point of its domain with positive derivative need not be non-decreasing. That is why we want to look for theorems for continuous functions.
2
Content available A note on weakly ϱ-upper continuous functions
EN
In the article we present definition and some properties of weakly ϱ-upper continuous functions. We find maximal additive and maximal multiplicative families for the class of weakly ϱ-upper continuous functions.
3
Content available On the almost uniform convergence
EN
Uniform convergence for continuous real functions sequences preserves continuity of the limit of such sequences. There are weaker types of convergence which have similar properties. We consider such types of convergence for functions from one topological space into another one.
EN
In the presented paper we study some properties of preponderantly continuous functions and functions satisfying the property A1. For any family F of real-valued functions we define MAXF = {g: max{f,g} ∈ F for all f ∈ F} and MINF = {g: min{f,g} ∈ F for all f ∈ F}. The aim of the paper is to find MINF for two discussed classes of functions.
5
Content available remote Perfectly continuous functions
EN
A new class of functions called [...]perfectly continuous functions is introduced and their basic properties are studied. Their place in the hierarchy of other variants of continuity that already exist in the literature is elaborated. Further, it is shown that if X is sum connected (e.g. connected or locally connected) and Y is Hausdorff, then the function space PA (X, Y] of all (...]-perfectly continuous functions from X into Y is closed in Yx in the topology of pointwise convergence.
6
Content available remote Maximal classes for the family of quasi-continuous functions with closed graph
EN
In this paper we consider classes of functions f : R - R. The maximal additive class for the family QU of quasi-continuous functions with closed graph is equal to the class of all continuous functions. We also show that the maximal multiplicative class for QU is equal to a class of continuous functions, which fulfil an extra condition.
7
Content available remote On some new decompositions of continuity
EN
The main purpose of this paper is to introduce the concepts of [...] to obtain new decompositions of continuity and super-continuity.
8
Content available remote On some forms of weakly continuous functions in bitopological spaces
EN
As a generalization of weakly continuous functions, we introduce the notion of (i, j)-weakly m-continuous functions in bitopological spaces and obtain unified characterizations and properties of certain forms of weakly continuous functions in bitopological spaces.
9
Content available remote On an extension for functions
EN
A new classes of functions, called strongly na-precontinuous functions, strongly na-continuous functions and na-continuous functions have been introduced. This paper considers the class of sigmas -na-continuous functions and its relationships to semi-regularization topologies, the other related functions. Preservation of appropriate topo-logical properties by sigmas -na-continuous functions is investigated.
10
Content available remote Some properties of upper and lower θ-quasicontinuous multifunctions
EN
In this paper we obtain new characterizations of upper and lower θ-quasicontinuous muitifunctions and investigate several properties of such multifunctions.
11
Content available remote Slightly beta-continuous multifunctions
EN
In this paper, we introduce and study upper and lower slightly beta-continuous multifunctions as a generalization of upper (lower) semicontinuous, upper (lower) alfa-continuous, upper (lower) precontinuous, upper (lower) quasi-continuous, upper (lower) gamma-continuous, upper (lower) beta-continuous multifunctions and slightly beta-continuous functions. Some characterizations and several properties concerning upper (lower) slightly beta-continuous multifunctions are obtained. Furthermore, the relationships between upper (lower) slightly beta-continuous multifunctions and other related multifunctions are also discussed.
12
Content available remote On the recursive sequence Xn+1=alfa+Xn-k:f(Xn,....Xn-k+1)
EN
The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation of the form Xn+l=alfa+Xn-k:f(Xn,....Xn-k+1, n=0, 1, ..... is investigated, where alfa > 0, k is an element of N and f : [0,infinity)- (0,infinity)k is a continuous function nondecreasing in each variable.
13
Content available remote On the notion of (gamma, s)-continuous functions
EN
In 2002, Noiri and Jafari studied the notion of (0, s-continuous functions due to Thompson [Proc. Amer. Math. Soc. 60 (1976) 335-338]. In this paper, a new generalization of (0, s-continuity which is called (gamma, s)-continuity is introduced and studied. Furthermore, characterizations, basic properties, preservation theorems of (gamma,s)- continuous functions and relationships between (gamma, s)-continuous functions and the other types of functions are investigated and obtained.
EN
In this article we investigate the maxima of two unilaterally approximately continuous and approximately regulated functions. In particular we prove that if / is the maximum of two unilaterally approximately continuous and approximately regulated functions then for each x is an element of Dunap(f) = {x : f is not unilaterally approximately continuous at x} the inequality f(x) < max(fap(x+),fap(x-)) holds. Moreover, we show some condition ensuring that an approximately regulated function f such that Dap(f) is countable and for each x is an element of Dunap(f) the inequality f(x) < max(fap(x+),fap(x-)) holds, is the maximum of two unilaterally approximately continuous and approximately regulated functions.
15
Content available remote On gamma alfa-continuous functions
EN
The aim of this paper is to introduce and study gamma alfa-continuous functions as a generalization of preirresoluteness, alfa-precontinuity, alfa-irresoluteness, gamma-irresoluteness, irresoluteness and semi alfa-irresoluteness. Furthermore, basic characterizations, preservation theorems and several properties concerning gamma alfa-continuous functions are investigated. The relationships between gamma alfa-continuous functions and the other types of continuity are also discussed.
16
Content available remote Characterization of continuous functions by class C(infinity) curves
EN
Let f : X -Y, where X is a Banach space and Y is a Hausdorff topological space. We prove that if f o (gamma) is continuous for every curve (gamma) : [0,1] -> X of class C(infinity), then f is continuous.
17
Content available remote On a weak form of almost weakly continuous functions
EN
A weak form of almost weak continuity, called subalmost weak continuity, is introduced. It is shown that subalmost weak continuity is strictly weaker than both almost weak continuity and subweak continuity. Subalmost weak continuity is used to improve a result in the literature concerning the graph of an almost weakly continuous function. Additional properties of these functions are also investigated.
18
Content available remote Wpływ zmian parametrów obiektu opisanego transmitacja G(s)=k /(Ts+1)ⁿ
PL
W pracy przedstawiono wpływ zmian rzędu n i stałej czasowej modelu T opisanego transmitacją [wzór] funkcjonały. Transmitacjami tymi opisuje się szereg obiektów przemysłowych. W przypadku występowania zmian ich parametrów w toku eksploatacji można stosować do sterowania układy adaptacyjne. Układy te mogą wykorzystać do sterowania zmiany przyjetego kryterium Q n1 lub Q.
EN
In this paper the influence of change of the parameters T and n of the transfer function [formula] to the two function criteria is considered. The transfer function described a series objects. The result may be used in system with self - tuning controllers.
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