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1
Content available remote Rate of convergence for Ibragimov-Gadjiev-Durrmeyer operators
Acar T.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
119--129
EN
The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include some well known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Here we estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.
2
Content available remote Superposition Operators in the Space of Functions of Waterman-Shiba Bounded Variation
Giménez J., Merentes N., Rodriguez L.
Commentationes Mathematicae
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2014
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Vol 54, No. 1
79--93
EN
In this paper we present a necessary condition for an autonomous superposition operator to act in the space of functions of Waterman-Shiba bounded variation. We also show that if a (general) superposition operator applies such space into itself and it is uniformly bounded, then its generating function satisfies a weak Matkowski condition.
3
Content available remote A Companion of the generalized trapezoid inequality and applications
Alomari M. W.
Journal of Mathematics and Applications
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2013
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Vol. 36
5--15
EN
A sharp companion of the generalized trapezoid inequality is introduced. Applications to quadrature formula are pointed out.
4
Content available remote Some convergence results for nonlinear singular integral operators
Karsli H.
Demonstratio Mathematica
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2013
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Vol. 46, nr 4
729--740
EN
In this paper, we establish some pointwise convergence results for a family of certain nonlinear singular integral operators Tλf of the form (...), acting on functions with bounded (Jordan) variation on an interval [a, b] as λ→λ0. Here, the kernels (...) satisfy some suitable singularity assumptions. We remark that the present study is a continuation and extension of the study of pointwise approximation of the family of nonlinear singular integral operators (1) begun in [18].
5
Content available remote Functions of two variables with bounded φ-variation in the sense of Riesz
Aziz W., Leiva H., Merentes N., Sánchez J. L.
Journal of Mathematics and Applications
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2010
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Vol. 32
5-23
EN
In this paper we introduce the concept of bounded φ- variation function, in the sense of Riesz, dened in a rectangle [wzór]. We prove that the linear space [wzór] generated by the class [wzór] of all φ-bounded variation functions is a Banach algebra. Moreover, we give necessary and sucient conditions for the Nemytskii operator acting in the space [wzór] to be globally Lipschitz.
6
Content available remote A Representation Theorem for '-Bounded Variation of Functions in the Sense of Riesz
Aziz W., Leiva H., Merentes N., Rzepka B.
Commentationes Mathematicae
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2010
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Vol. 50, [Z] 2
109-120
EN
In this paper we extend the well known Riesz lemma to the class of bounded φ-variation functions in the sense of Riesz defined on a rectangle [...].This concept was introduced in [2], where the authors proved that the space [...] of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].
7
Content available remote Generalized Köthe-Toeplitz dual of some double sequence spaces
Tripathy B. C., Sarma B.
Fasciculi Mathematici
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2008
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Nr 40
119-125
EN
In this article we introduce the notion of η-dual of double sequence spaces. We find the η-dual of some double sequence spaces. We verify the perfectness of different double sequence spaces relative to η-dual.
8
Content available remote On fuzzy number calculus
Kosiński W.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 1
51-57
EN
Some generalizations of the concept of ordered fuzzy numbers (OFN) are defined to handle fuzzy inputs in a quantitative way, exactly as real numbers are handled. Additional two structures, an algebraic one and a normed (topological) one, are introduced to allow for counting with a more general type of membership relations.
9
Content available remote On the Kantorovich variant of generalized Bernstein type rational functions
Gupta V., Ispir N.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
117-130
EN
In the present paper we define Kantorovich variant of generalized Bernstein type rational functions. We establish the order of approximation for continuous functions in different normed spaces and also estimate the rate of convergence for functions of bounded variation.
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