International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111720180516Weakly invariant subspaces for multivalued linear operators on Banach spaces877884http://dx.doi.org/10.22436/jnsa.011.07.01ENGerald WanjalaDepartment of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, PC 123, Al Khoud, Sultanate of OmanPeter Saveliev generalized Lomonosov's invariant subspace theorem to the case of linear relations. In particular, he proved that if \(\mathcal S\) and \(\mathcal T\) are linear relations defined on a Banach space \(X\) and having finite dimensional multivalued parts and if \(\mathcal T\) right commutes with \(\mathcal S\), that is, \(\mathcal S \mathcal T \subset \mathcal T\mathcal S\), and if \(\mathcal S\) is compact then \(\mathcal T\) has a nontrivial weakly invariant subspace. However, the case of left commutativity remained open. In this paper, we develop some operator representation techniques for linear relations and use them to solve the left commutativity case mentioned above under the assumption that \(\mathcal S\mathcal T(0) = \mathcal S(0)\) and \(\mathcal T\mathcal S(0) = \mathcal T(0)\).http://www.isr-publications.com/jnsa/7079/download-weakly-invariant-subspaces-for-multivalued-linear-operators-on-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111720180516Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach885893http://dx.doi.org/10.22436/jnsa.011.07.02EN MarijaRašajskiSchool of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11000 Belgrade, SerbiaTatjana LutovacSchool of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11000 Belgrade, SerbiaBrankoMaleševićSchool of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11000 Belgrade, SerbiaIn this paper, we propose and prove some generalizations and sharpenings of certain inequalities
of Wilker's and Shafer-Fink's type. Application of the Wu-Debnath
theorem enabled us to prove some double sided inequalities.http://www.isr-publications.com/jnsa/7080/download-sharpening-and-generalizations-of-shafer-fink-and-wilker-type-inequalities-a-new-approachInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111720180517Superstability of Kannappan's and Van vleck's functional equations894915http://dx.doi.org/10.22436/jnsa.011.07.03ENBelfakih KeltoumaUniversity Ibn Zohr, Faculty of Sciences, Department of Mathematics, Agadir, MoroccoElqorachi ElhoucienUniversity Ibn Zohr, Faculty of Sciences, Department of Mathematics, Agadir, MoroccoThemistocles M. RassiasDepartment of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, GreeceRedouani AhmedUniversity Ibn Zohr, Faculty of Sciences, Department of Mathematics, Agadir, MoroccoIn this paper, we prove the superstability theorems of the
functional equations
\[\mu(y)f(x\sigma(y)z_0)\pm f(xyz_0) =2f(x)f(y), \;x,y\in S,\quad
\mu(y)f( \sigma(y)xz_0)\pm f(xyz_0) = 2f(x)f(y), \;x,y\in S,\]
where \(S\) is a semigroup, \(\sigma\) is an involutive morphism of \(S\),
and \(\mu:\) \(S\longrightarrow \mathbb{C}\) is a bounded multiplicative
function such that \(\mu(x\sigma(x))=1\) for all \(x \in S\), and
\(z_{0}\) is in the center of \(S\).http://www.isr-publications.com/jnsa/7083/download-superstability-of-kannappans-and-van-vlecks-functional-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111720180517On the existence problem of solutions to a class of fuzzy mixed exponential vector variational inequalities 916926http://dx.doi.org/10.22436/jnsa.011.07.04ENShih-Sen ChangCenter for General Education, China Medical University, Taichung 40402, TaiwanSalahuddinDepartment of Mathematics, Jazan University, Jazan, Kingdom of Saudi ArabiaChing-Feng Wen Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan \(\&\) Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, TaiwanXiong Rui WangDepartment of Mathematics,Yibin University, Yibin, Sichuan 644007, ChinaIn this research article, we deal with a new kind of mixed
exponential fuzzy vector variational inequalities in ordered
Euclidean spaces. By using KKM-technique and Nadler's fixed point
theorem, we prove some existence theorems of solutions to mixed
exponential vector variational inequality problems in fuzzy
environment.
http://www.isr-publications.com/jnsa/7084/download-on-the-existence-problem-of-solutions-to-a-class-of-fuzzy-mixed-exponential-vector-variational-inequalities