<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we initiate and explore the interesting characterizations and properties of fuzzy soft almost soft continuous mappings in fuzzy soft classes. We also study and discuss the notions of fuzzy soft almost soft open(closed) mappings. Moreover the characterizations of composition of two fuzzy soft almost soft mappings are also studied. We hope that the findings in this paper will be useful for the researchers working in the fields such as fuzzy control systems, fuzzy automata, fuzzy logic, information systems and decision making problems.</abstract>

On Some Properties of Fuzzy Soft almost Soft Continuous Mappings

<abstract xmlns="http://www.w3.org/1999/xhtml">The main objective of this research is to characterize all the real polynomial functions of degree less than the fourth which are Jensen <italic>m</italic>-convex on the set of non-negative real numbers. In the first section, it is established for that class of functions what conditions must satisfy a particular polynomial in order to be starshaped on the same set. Finally, both kinds of results are combined in order to find examples of either Jensen <italic>m</italic>-convex functions which are not starshaped or viceversa.</abstract>

On the characterization of Jensen <italic>m</italic>-convex polynomials

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0013_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>τ</mi></mrow></msubsup></mrow></math><tex-math>$B_{p,q}^{s,\tau }$</tex-math></alternatives></inline-formula>, containing as special cases: Goldberg space <italic>bmo</italic>, local Morrey-Campanato spaces <italic>l</italic>2,<italic>λ</italic> and the classical Hölder and Besov spaces <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0013_eq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mi>s</mi></msubsup></mrow></math><tex-math>$B_{p,q}^s $</tex-math></alternatives></inline-formula>. This work extends the results of [<xref ref-type="bibr" rid="j_mjpaa-2017-0013_ref_013_w2aab3b7b3b1b6b1ab1ac13Aa">13</xref>, <xref ref-type="bibr" rid="j_mjpaa-2017-0013_ref_002_w2aab3b7b3b1b6b1ab1ab2Aa">2</xref>, <xref ref-type="bibr" rid="j_mjpaa-2017-0013_ref_015_w2aab3b7b3b1b6b1ab1ac15Aa">15</xref>] from Hölder and Besov spaces to the general frame of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0013_eq_003.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>τ</mi></mrow></msubsup></mrow></math><tex-math>$B_{p,q}^{s,\tau }$</tex-math></alternatives></inline-formula> spaces.</abstract>

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, the notion of new generalized (<italic>s, m, ϕ</italic>)-preinvex mapping is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving new generalized (<italic>s, m, ϕ</italic>)-preinvex mappings along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for new generalized (<italic>s, m, ϕ</italic>)-preinvex mappings via conformable fractional integrals are established. At the end, some applications to special means are given.</abstract>

New conformable fractional integrals of Ostrowski type using new generalized (<italic>s, m, ϕ</italic>)-preinvex mappings

<abstract xmlns="http://www.w3.org/1999/xhtml">We consider the perturbed nonlinear boundary condition problem<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0015_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mo>-</mo><msub><mi>Δ</mi><mi>p</mi></msub><mi>u</mi></mrow></mtd><mtd><mo>=</mo></mtd><mtd><mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mrow><mi>λ</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>u</mi></mrow><mo>)</mo></mrow><mi> </mi><mtext>in</mtext><mi> </mi><mi>Ω</mi></mrow></mtd></mtr><mtr><mtd><mrow><msup><mrow><mrow><mo>|</mo><mrow><mo>∇</mo><mi>u</mi></mrow><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi><mo>.</mo><mi>ν</mi></mrow></mtd><mtd><mo>=</mo></mtd><mtd><mrow><mi>λ</mi><mi>ρ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mi> </mi><mtext>on</mtext><mi> </mi><mi>Γ</mi><mo>.</mo></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math><tex-math>$$\left\{ {\matrix{ { - \Delta _p u} \hfill &amp; = \hfill &amp; {\left| u \right|^{p - 2} u + f\left( {\lambda ,x,u} \right)\,{\rm{in}}\,\Omega } \hfill \cr {\left| {\nabla u} \right|^{p - 2} \nabla u.\nu } \hfill &amp; = \hfill &amp; {\lambda \rho \left( x \right)\left| u \right|^{p - 2} u\,{\rm{on}}\,\Gamma .} \hfill \cr } } \right.$$</tex-math></alternatives></disp-formula>Using the Sobolev trace embedding and the duality mapping defined on <italic>W</italic>1,<italic>p</italic>(Ω), we prove that this problem bifurcates from the principal eigenvalue <italic>λ</italic>1 of the eigenvalue problem<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0015_eq_002.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mo>-</mo><msub><mi>Δ</mi><mi>p</mi></msub><mi>u</mi></mrow></mtd><mtd><mo>=</mo></mtd><mtd><mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mi> </mi><mtext>in</mtext><mi> </mi><mi>Ω</mi></mrow></mtd></mtr><mtr><mtd><mrow><msup><mrow><mrow><mo>|</mo><mrow><mo>∇</mo><mi>u</mi></mrow><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi><mo>.</mo><mi>ν</mi></mrow></mtd><mtd><mo>=</mo></mtd><mtd><mrow><mi>λ</mi><mi>ρ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mi> </mi><mtext>on</mtext><mi> </mi><mi>Γ</mi><mo>.</mo></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math><tex-math>$$\left\{ {\matrix{ { - \Delta _p u} \hfill &amp; = \hfill &amp; {\left| u \right|^{p - 2} u\,{\rm{in}}\,\Omega } \hfill \cr {\left| {\nabla u} \right|^{p - 2} \nabla u.\nu } \hfill &amp; = \hfill &amp; {\lambda \rho \left( x \right)\left| u \right|^{p - 2} u\,{\rm{on}}\,\Gamma .} \hfill \cr } } \right.$$</tex-math></alternatives></disp-formula></abstract>

A bifurcation result involving Sobolev trace embedding and the duality mapping of <italic>W</italic>1<italic>,p</italic>

<abstract xmlns="http://www.w3.org/1999/xhtml">The major emphasis of this work is the derivation of a posteriori error estimates for the mixed finite volume discretization of second-order elliptic equations. The estimates are established for meshes consisting of simplices on unstructured grids. We consider diffusion problems with nonhomogeneous diffusion coefficients. The error estimates are of residual types and are formulated in the energy semi-norm for a locally postprocessed approximate solutions. The estimates are fully computable and locally efficient that they can serve as indicators for adaptive refinement and for the actual control of the error. Numerical results are shown for two test examples in two space dimensions. It is found that the proposed adaptive mixed finite volume method offers a robust and accurate approach for solving second-order elliptic equations, even when highly nonhomogeneous diffusion coefficients are used in the simulations.</abstract>

Université Paris 13, Sorbonne Paris Cité

Laboratory of Complex Systems Engineering & Human Systems

School of Engineering and Computing Sciences

Université des sciences, des techniques et des technologies de Bamako

A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

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Moroccan Journal of Pure and Applied Analysis

 The Moroccan Journal of Pure and Applied Analysis "MJPAA" (Print ISSN: 2605-6364) is a peer-reviewed open access journal published by the "Université Sidi Mohamed Ben Abdellah" (Sidi Mohamed Ben Abdallah University), covering all main-stream branches of pure and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, numerical analysis, optimization theory, and control theory.   MJPAA is published by Sidi Mohamed Ben Abdallah University in three issues in January, May and September.   Why subscribe and read    The journal covers a wide range of branches of mathematical analysis.   Pure and applied analysis topics are intensely studied by researchers throughout the world especially in Africa, the Arab and European countries.   An edition committee of high-level and international renown.   Editorial board representing different regions of the world and various research teams.      Why submit    No publication charges for the authors or their institutions.   The journal is available to be indexed in the most important databases.   The journal is among the best in its field in Africa and the Arab world.      Rejection Rate    45%      Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.   Publisher:Sidi Mohamed Ben Abdallah University (Route Imouzzer, BP 2626 Fez 30000, Morocco, Tel. : 0212 5 35 60 96 60/ 61)   Contact:Professor Youssef Akdim, Sidi Mohamed Ben Abdellah Universitymjpaa.edition1@usmba.ac.ma 

Moroccan Journal of Pure and Applied Analysis

Volume 3 (2017): Issue 2 (December 2017)

On Some Properties of Fuzzy Soft almost Soft Continuous Mappings

On the characterization of Jensen m-convex polynomials

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

New conformable fractional integrals of Ostrowski type using new generalized (s, m, ϕ)-preinvex mappings

A bifurcation result involving Sobolev trace embedding and the duality mapping of W¹^,p

A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

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All Volumes and Issues in this Journal

Moroccan Journal of Pure and Applied Analysis

Volume 3 (2017): Issue 2 (December 2017)

On Some Properties of Fuzzy Soft almost Soft Continuous Mappings

On the characterization of Jensen m-convex polynomials

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

New conformable fractional integrals of Ostrowski type using new generalized (s, m, ϕ)-preinvex mappings

A bifurcation result involving Sobolev trace embedding and the duality mapping of W1,p

A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

Search

All Volumes and Issues in this Journal

A bifurcation result involving Sobolev trace embedding and the duality mapping of W¹^,p