Janusz Brzdek - Academia.edu (original) (raw)
Papers by Janusz Brzdek
Fixed Point Theory and Applications, Nov 8, 2013
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Publicationes Mathematicae Debrecen
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Advances in the Theory of Nonlinear Analysis and its Application, 2017
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Results in Mathematics, 2021
We present some applications of the Banach limit in the study of the stability of the linear func... more We present some applications of the Banach limit in the study of the stability of the linear functional equation in a single variable.
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Filomat, 2017
We show that some multifunctions F : K ? n(Y), satisfying functional inclusions of the form ? (x,... more We show that some multifunctions F : K ? n(Y), satisfying functional inclusions of the form ? (x,F(?1(x)),..., F(?n(x)))? F(x)G(x), admit near-selections f : K ? Y, fulfilling the functional equation ? (x,f (?1(x)),..,, f(?n(x)))= f(x), where functions G : K ? n(Y), ?: K x Yn ? Y and ?1,..., ?n ? KK are given, n is a fixed positive integer, K is a nonempty set, (Y,?) is a group and n(Y) denotes the family of all nonempty subsets of Y. Our results have been motivated by the notion of Ulam stability and some earlier outcomes. The main tool in the proofs is a very recent fixed point theorem for nonlinear operators, acting on some spaces of multifunctions.
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Aequationes mathematicae, 2018
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Demonstratio Mathematica, 2010
We prove the Hyers–Ulam stability, on restricted domain, of a functional equation of Jensen type,... more We prove the Hyers–Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).
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Fixed Point Theory, 2017
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Journal of Fixed Point Theory and Applications, 2017
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Bulletin of the Australian Mathematical Society, 2016
In this paper we present a simple (fixed point) method that yields various results concerning app... more In this paper we present a simple (fixed point) method that yields various results concerning approximate solutions of some difference equations. The results are motivated by the notion of Ulam stability.
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Journal of Function Spaces, 2016
This is a survey presenting the most significant results concerning approximate (generalized) der... more This is a survey presenting the most significant results concerning approximate (generalized) derivations, motivated by the notions of Ulam and Hyers-Ulam stability. Moreover, the hyperstability and superstability issues connected with derivations are discussed. In the section before the last one we highlight some recent outcomes on stability of conditions defining (generalized) Lie derivations.
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Aequationes mathematicae, 2014
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Pacific Journal of Mathematics, 2015
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Journal of Function Spaces and Applications, 2013
We prove some results for mappings taking values in ultrametric spaces and satisfying approximate... more We prove some results for mappings taking values in ultrametric spaces and satisfying approximately a generalization of the equation ofp-Wright affine functions. They are motivated by the notion of stability for functional equations.
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TheScientificWorldJournal, 2014
We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x)... more We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.
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Journal of Function Spaces and Applications, 2013
We prove some stability and hyperstability results for the well-known Fréchet equation stemming f... more We prove some stability and hyperstability results for the well-known Fréchet equation stemming from one of the characterizations of the inner product spaces. As the main tool, we use a fixed point theorem for the function spaces. We finish the paper with some new inequalities characterizing the inner product spaces.
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Discrete Dynamics in Nature and Society, 2014
This is a survey paper concerning stability results for the linear functional equation in single ... more This is a survey paper concerning stability results for the linear functional equation in single variable. We discuss issues that have not been considered or have been treated only briefly in other surveys concerning stability of the equation. In this way, we complement those surveys.
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Journal of Function Spaces, 2014
The fixed point method has been applied for the first time, in proving the stability results for ... more The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.
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We show that generalizations of some (classical) results on the Hyers-Ulam stabil- ity of functio... more We show that generalizations of some (classical) results on the Hyers-Ulam stabil- ity of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.
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Journal of Mathematical Analysis and Applications, 2011
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Fixed Point Theory and Applications, Nov 8, 2013
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Publicationes Mathematicae Debrecen
Bookmarks Related papers MentionsView impact
Advances in the Theory of Nonlinear Analysis and its Application, 2017
Bookmarks Related papers MentionsView impact
Results in Mathematics, 2021
We present some applications of the Banach limit in the study of the stability of the linear func... more We present some applications of the Banach limit in the study of the stability of the linear functional equation in a single variable.
Bookmarks Related papers MentionsView impact
Filomat, 2017
We show that some multifunctions F : K ? n(Y), satisfying functional inclusions of the form ? (x,... more We show that some multifunctions F : K ? n(Y), satisfying functional inclusions of the form ? (x,F(?1(x)),..., F(?n(x)))? F(x)G(x), admit near-selections f : K ? Y, fulfilling the functional equation ? (x,f (?1(x)),..,, f(?n(x)))= f(x), where functions G : K ? n(Y), ?: K x Yn ? Y and ?1,..., ?n ? KK are given, n is a fixed positive integer, K is a nonempty set, (Y,?) is a group and n(Y) denotes the family of all nonempty subsets of Y. Our results have been motivated by the notion of Ulam stability and some earlier outcomes. The main tool in the proofs is a very recent fixed point theorem for nonlinear operators, acting on some spaces of multifunctions.
Bookmarks Related papers MentionsView impact
Aequationes mathematicae, 2018
Bookmarks Related papers MentionsView impact
Demonstratio Mathematica, 2010
We prove the Hyers–Ulam stability, on restricted domain, of a functional equation of Jensen type,... more We prove the Hyers–Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).
Bookmarks Related papers MentionsView impact
Fixed Point Theory, 2017
Bookmarks Related papers MentionsView impact
Journal of Fixed Point Theory and Applications, 2017
Bookmarks Related papers MentionsView impact
Bulletin of the Australian Mathematical Society, 2016
In this paper we present a simple (fixed point) method that yields various results concerning app... more In this paper we present a simple (fixed point) method that yields various results concerning approximate solutions of some difference equations. The results are motivated by the notion of Ulam stability.
Bookmarks Related papers MentionsView impact
Journal of Function Spaces, 2016
This is a survey presenting the most significant results concerning approximate (generalized) der... more This is a survey presenting the most significant results concerning approximate (generalized) derivations, motivated by the notions of Ulam and Hyers-Ulam stability. Moreover, the hyperstability and superstability issues connected with derivations are discussed. In the section before the last one we highlight some recent outcomes on stability of conditions defining (generalized) Lie derivations.
Bookmarks Related papers MentionsView impact
Aequationes mathematicae, 2014
Bookmarks Related papers MentionsView impact
Pacific Journal of Mathematics, 2015
Bookmarks Related papers MentionsView impact
Journal of Function Spaces and Applications, 2013
We prove some results for mappings taking values in ultrametric spaces and satisfying approximate... more We prove some results for mappings taking values in ultrametric spaces and satisfying approximately a generalization of the equation ofp-Wright affine functions. They are motivated by the notion of stability for functional equations.
Bookmarks Related papers MentionsView impact
TheScientificWorldJournal, 2014
We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x)... more We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.
Bookmarks Related papers MentionsView impact
Journal of Function Spaces and Applications, 2013
We prove some stability and hyperstability results for the well-known Fréchet equation stemming f... more We prove some stability and hyperstability results for the well-known Fréchet equation stemming from one of the characterizations of the inner product spaces. As the main tool, we use a fixed point theorem for the function spaces. We finish the paper with some new inequalities characterizing the inner product spaces.
Bookmarks Related papers MentionsView impact
Discrete Dynamics in Nature and Society, 2014
This is a survey paper concerning stability results for the linear functional equation in single ... more This is a survey paper concerning stability results for the linear functional equation in single variable. We discuss issues that have not been considered or have been treated only briefly in other surveys concerning stability of the equation. In this way, we complement those surveys.
Bookmarks Related papers MentionsView impact
Journal of Function Spaces, 2014
The fixed point method has been applied for the first time, in proving the stability results for ... more The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.
Bookmarks Related papers MentionsView impact
We show that generalizations of some (classical) results on the Hyers-Ulam stabil- ity of functio... more We show that generalizations of some (classical) results on the Hyers-Ulam stabil- ity of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.
Bookmarks Related papers MentionsView impact
Journal of Mathematical Analysis and Applications, 2011
Bookmarks Related papers MentionsView impact