<abstract xmlns="http://www.w3.org/1999/xhtml">The purpose of this note is to discuss the recent paper of Espínola and Wiśnicki about the fixed point theory of monotone nonexpansive mappings. In their work, it is claimed that most of the fixed point results of this class of mappings boil down to the classical Knaster-Tarski fixed point theorem. We will show that their approach is very restrictive and fail to have any meaningful usefulness in applications.</abstract>

Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we define and investigate soft real point matrices and their operations which are more functional to make theoretical studies in the soft real point set theory. We then define products of soft real point matrices and their properties. Examples are also provided to validate the existence of defined notions.</abstract>

Department of Mathematics, College of Science

On Soft Real Point Matrices and Their Operations

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper the periodic even functions for which all the regular Riemann sums vanishe are called special periodic even functions. A construction of some of them is put forward, this one rest on the Fourier serie and H. Davenport’s estimations concerning the Moebius function. The special periodic even functions seem linked to the number theory, as this can be seen on the Fourier serie result, on the proposed constructions and on the proof that such functions cannot belong to the Wiener algebra.</abstract>

Special Periodic Even Functions

<abstract xmlns="http://www.w3.org/1999/xhtml">In this work, <italic>Lp</italic>-error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are given. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals.</abstract>

Department of Mathematics, Faculty of Science and Information Technology

Laboratoire de Mathématiques et de leurs Applications

Université de Pau et des Pays de l’Adour

<italic>Lp</italic> –Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

<abstract xmlns="http://www.w3.org/1999/xhtml">In this note, we point out some minor errors found in [1] and we give the proper corrections.</abstract>

Erratum to: A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces; DOI 10.1515/mjpaa-2017-0013

<abstract xmlns="http://www.w3.org/1999/xhtml">We consider the nonlocal eigenvalue problem of the following form<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2018-0006_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>𝒫</mi><mi>k</mi><mo>)</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msubsup><mrow><mi>𝒧</mi></mrow><mi>K</mi><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msubsup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><msup><mrow><mrow><mrow><mo>|</mo><mrow><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></mrow><mrow><mover><mi>p</mi><mo>¯</mo></mover><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mtd><mtd><mo>=</mo></mtd><mtd><mrow><mi>λ</mi><msup><mrow><mrow><mrow><mo>|</mo><mrow><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></mrow><mrow><mi>r</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mtd><mtd><mrow><mi>i</mi><mi>n</mi></mrow></mtd><mtd><mrow><mi>Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mi>u</mi></mtd><mtd><mo>=</mo></mtd><mtd><mn>0</mn></mtd><mtd><mrow><mi>i</mi><mi>n</mi></mrow></mtd><mtd><mrow><msup><mrow><mtext>𝕉</mtext></mrow><mi>N</mi></msup><mo>\</mo><mi>Ω</mi><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math><tex-math>$$(\mathcal{P}k)\left\{ {\matrix{ {\mathcal{L}_K^{p(x)}u(x) + {{\left| {u(x)} \right|}^{\bar p(x) - 2}}u(x)} \hfill &amp; = \hfill &amp; {\lambda {{\left| {u(x)} \right|}^{r(x) - 2}}u(x)} \hfill &amp; {in} \hfill &amp; {\Omega ,} \hfill \cr u \hfill &amp; = \hfill &amp; 0 \hfill &amp; {in} \hfill &amp; {{{\rm\mathbb{R}}^N}\backslash \Omega ,} \hfill \cr } } \right.$$</tex-math></alternatives></disp-formula>where Ω is a smooth open and bounded set in 𝕉<italic>N</italic> (<italic>N</italic> ⩾ 3), λ <italic>></italic> 0 is a real number, <italic>K</italic> is a suitable kernel and <italic>p</italic>, <italic>r</italic> are two bounded continuous functions on ̄Ω. The main result of this paper establishes that any λ <italic>></italic> 0 sufficiently small is an eigenvalue of the above nonhomogeneous nonlocal problem. The proof relies on some variational arguments based on Ekeland's variational principle.</abstract>

Nonlocal eigenvalue problems with variable exponent

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Moroccan Journal of Pure and Applied Analysis

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Moroccan Journal of Pure and Applied Analysis

Volume 4 (2018): Issue 1 (June 2018)

Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings

On Soft Real Point Matrices and Their Operations

Special Periodic Even Functions

L^p –Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

Erratum to: A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces; DOI 10.1515/mjpaa-2017-0013

Nonlocal eigenvalue problems with variable exponent

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All Volumes and Issues in this Journal

Moroccan Journal of Pure and Applied Analysis

Volume 4 (2018): Issue 1 (June 2018)

Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings

On Soft Real Point Matrices and Their Operations

Special Periodic Even Functions

Lp –Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

Erratum to: A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces; DOI 10.1515/mjpaa-2017-0013

Nonlocal eigenvalue problems with variable exponent

Search

All Volumes and Issues in this Journal

L^p –Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals