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Prof. Dr. Janusz Brzdek

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Guest Editor

Department of Mathematics, Pedagogical University, Podchorazych 2, 30-084 Krakow, Poland
Interests: functional equations and inequalities; Ulam's type stability; fixed point theory

Prof. Dr. Shahram Shahram Rezapour

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Guest Editor

1. Department of Medical Research, China Medical University, Taichung, Taiwan
2. Department of Mathematics, Azerbaijan Shahid Madani University, Tabriz, Iran
Interests: approximation theory; fixed point theory; fractional differential equations; fractional finite difference equations
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Special Issue Information

Dear Colleagues,

It is very well known that stability problems are very important in the numerical solving of fractional integro-differential equations using different modern computer programs. However, similar issues also arise in many other areas of pure and applied mathematics. This Special Issue deals mainly with the theoretical approaches to such problems; especially, any work including new ideas or notions, novelty techniques and/or results on stability of singular fractional integro-differential equations are welcome. We accept high-quality research or review papers.

The purpose of this Special Issue is to connect somehow efforts of various scientists, for whom stability problems are important in their research activity; in particular mathematicians and computer engineers.

Prof. Dr. Janusz Brzdek
Prof. Dr. Shahram Rezapour
Guest Editors

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Keywords

fractional differential equations
integral equations
Hyers-Ulam Stability
stability problems
Ulam's type stability

Published Papers (3 papers)

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Research

19 pages, 291 KiB

Open AccessArticle

Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability

by Badr Alqahtani, Andreea Fulga and Erdal Karapınar

Mathematics 2018, 6(10), 208; https://doi.org/10.3390/math6100208 - 17 Oct 2018

Cited by 43 | Viewed by 2847

Abstract

In this paper, in the setting of

Δ

In this paper, in the setting of

Δ

-symmetric quasi-metric spaces, the existence and uniqueness of a fixed point of certain operators are scrutinized carefully by using simulation functions. The most interesting side of such operators is that they do not form a contraction. As an application, in the same framework, the Ulam stability of such operators is investigated. We also propose some examples to illustrate our results. Full article

(This article belongs to the Special Issue Stability Problems)

11 pages, 211 KiB

Open AccessArticle

Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

by Elhoucien Elqorachi and Michael Th. Rassias

Mathematics 2018, 6(5), 83; https://doi.org/10.3390/math6050083 - 18 May 2018

Cited by 12 | Viewed by 2735

Abstract

In the present paper we study the generalized Hyers–Ulam stability of the generalized trigonometric functional equations [...] Read more.

In the present paper we study the generalized Hyers–Ulam stability of the generalized trigonometric functional equations

f (x y) + μ (y) f (x σ (y)) = 2 f (x) g (y) + 2 h (y), x, y \in S;

f (x y) + μ (y) f (x σ (y)) = 2 f (y) g (x) + 2 h (x), x, y \in S,

where S is a semigroup,

σ

S ⟶ S

is a involutive morphism, and

μ

S ⟶ C

is a multiplicative function such that

μ (x σ (x)) = 1

for all

x \in S .

As an application, we establish the generalized Hyers–Ulam stability theorem on amenable monoids and when

σ

is an involutive automorphism of S. Full article

(This article belongs to the Special Issue Stability Problems)

12 pages, 260 KiB

Open AccessArticle

Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces

by Mohammad Maleki V., S. Mansour Vaezpour and Reza Saadati

Mathematics 2018, 6(2), 22; https://doi.org/10.3390/math6020022 - 09 Feb 2018

Cited by 5 | Viewed by 2882

Abstract

In this paper, we prove the generalized nonlinear stability of the first and second of the following

ρ

-functional equations, [...] Read more.

In this paper, we prove the generalized nonlinear stability of the first and second of the following

ρ

-functional equations,

G (| a | Δ_{A}^{*} | b |) Δ_{B}^{*} G (| a | Δ_{A}^{* *} | b |) - G (| a |) Δ_{B}^{* *} G (| b |) = ρ (2 [G, (\frac{| a | Δ_{A}^{*} | b |}{2}), Δ_{B}^{*}, G, (\frac{| a | Δ_{A}^{* *} | b |}{2})] - G (| a |) Δ_{B}^{* *} G (| b |))

, and

2 [G, (\frac{| a | Δ_{A}^{*} | b |}{2}), Δ_{B}^{*}, G, (\frac{| a | Δ_{A}^{* *} | b |}{2})] - G (| a |) Δ_{B}^{* *} G (| b |) = ρ (G (| a | Δ_{A}^{*} | b |) Δ_{B}^{*} G (| a | Δ_{A}^{* *} | b |) - G (| a |) Δ_{B}^{* *} G (| b |))

in latticetic random Banach lattice spaces, where

ρ

is a fixed real or complex number with

ρ \neq 1

. Full article

(This article belongs to the Special Issue Stability Problems)

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