Janusz Brzdek - Academia.edu (original) (raw)

Papers by Janusz Brzdek

Research paper thumbnail of Stability of additivity and fixed point methods

Fixed Point Theory and Applications, Nov 8, 2013

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Research paper thumbnail of On continuous solutions and stability of a conditional Goąb--Schinzel equation

Publicationes Mathematicae Debrecen

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Research paper thumbnail of Remarks on solutions to the functional equations of the radical type

Advances in the Theory of Nonlinear Analysis and its Application, 2017

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Research paper thumbnail of Banach Limit in the Stability Problem of a Linear Functional Equation

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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Research paper thumbnail of Ulam stability of some functional inclusions for multi-valued mappings

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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Research paper thumbnail of Remarks on solutions to a generalization of the radical functional equations

Aequationes mathematicae, 2018

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Research paper thumbnail of A note on stability of the Popoviciu functional equation on restricted domain

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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Research paper thumbnail of Approximately <i>p</i>-Wright affine functions, inner product spaces and derivations

Fixed Point Theory, 2017

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Research paper thumbnail of Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability

Journal of Fixed Point Theory and Applications, 2017

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Research paper thumbnail of On Approximate Solutions of Some Difference equations

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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Research paper thumbnail of Survey on Recent Ulam Stability Results Concerning Derivations

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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Research paper thumbnail of Remarks on stability of some inhomogeneous functional equations

Aequationes mathematicae, 2014

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Research paper thumbnail of Fixed-point results and the Hyers–Ulam stability of linear equations of higher orders

Pacific Journal of Mathematics, 2015

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Research paper thumbnail of On Approximatelyp-Wright Affine Functions in Ultrametric Spaces

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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Research paper thumbnail of On Ulam's type stability of the Cauchy additive equation

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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Research paper thumbnail of Hyperstability of the Fréchet Equation and a Characterization of Inner Product Spaces

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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Research paper thumbnail of On Ulam’s Type Stability of the Linear Equation and Related Issues

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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Research paper thumbnail of Fixed Point Theory and the Ulam Stability

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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Research paper thumbnail of On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains

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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Research paper thumbnail of On approximate solutions of the linear functional equation of higher order

Journal of Mathematical Analysis and Applications, 2011

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Research paper thumbnail of Stability of additivity and fixed point methods

Fixed Point Theory and Applications, Nov 8, 2013

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On continuous solutions and stability of a conditional Goąb--Schinzel equation

Publicationes Mathematicae Debrecen

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Remarks on solutions to the functional equations of the radical type

Advances in the Theory of Nonlinear Analysis and its Application, 2017

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Banach Limit in the Stability Problem of a Linear Functional Equation

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

Research paper thumbnail of Ulam stability of some functional inclusions for multi-valued mappings

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

Research paper thumbnail of Remarks on solutions to a generalization of the radical functional equations

Aequationes mathematicae, 2018

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A note on stability of the Popoviciu functional equation on restricted domain

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

Research paper thumbnail of Approximately <i>p</i>-Wright affine functions, inner product spaces and derivations

Fixed Point Theory, 2017

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Research paper thumbnail of Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability

Journal of Fixed Point Theory and Applications, 2017

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On Approximate Solutions of Some Difference equations

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

Research paper thumbnail of Survey on Recent Ulam Stability Results Concerning Derivations

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

Research paper thumbnail of Remarks on stability of some inhomogeneous functional equations

Aequationes mathematicae, 2014

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fixed-point results and the Hyers–Ulam stability of linear equations of higher orders

Pacific Journal of Mathematics, 2015

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On Approximatelyp-Wright Affine Functions in Ultrametric Spaces

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

Research paper thumbnail of On Ulam's type stability of the Cauchy additive equation

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

Research paper thumbnail of Hyperstability of the Fréchet Equation and a Characterization of Inner Product Spaces

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

Research paper thumbnail of On Ulam’s Type Stability of the Linear Equation and Related Issues

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

Research paper thumbnail of Fixed Point Theory and the Ulam Stability

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

Research paper thumbnail of On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains

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

Research paper thumbnail of On approximate solutions of the linear functional equation of higher order

Journal of Mathematical Analysis and Applications, 2011

Bookmarks Related papers MentionsView impact