International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111620180406On \(m\)-skew complex symmetric operators734745http://dx.doi.org/10.22436/jnsa.011.06.01ENHaiying LiSchool of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. ChinaYaru WangSchool of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. ChinaIn this paper, the definition of \(m\)-skew complex symmetric operators is introduced. Firstly, we
prove that \(\Delta_{m}^{-}(T)\) is complex symmetric with the
conjugation \(C\) and give some properties of \(\Delta_{m}^{-}(T)\).
Secondly, let \(T\) be \(m\)-skew complex symmetric
with conjugation \(C\), if \(n\) is odd, then \(T^{n}\) is \(m\)-skew complex symmetric
with conjugation \(C\); if \(n\) is even, with the assumption \(T^{*}CTC=CTCT^{*}\),
then \(T^{n}\) is \(m\)-complex symmetric
with conjugation \(C\). Finally, we give some properties of \(m\)-skew complex
symmetric operators.http://isr-publications.com/jnsa/6987/download-on-m-skew-complex-symmetric-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111620180413The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces746761http://dx.doi.org/10.22436/jnsa.011.06.02ENChaichana JaiboonDepartment of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, ThailandSomyot PlubtiengDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandPhayap KatchangDivision of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, ThailandIn this research, we focus on a common fixed point problem of a
nonexpansive semigroup with the generalized viscosity methods for
implicit iterative algorithms. Our main objective is to construct
the new strong convergence theorems under certain appropriate
conditions in uniformly convex and uniformly smooth Banach spaces.
Specifically, the main results make a contribution to the implicit
midpoint theorems. The findings for theorems in Hilbert spaces and
the other forms of a nonexpansive semigroup can be used in several
practical purposes. Finally, a numerical example in 3 dimensions is
provided to support our main results. http://isr-publications.com/jnsa/7006/download-the-generalized-viscosity-implicit-rule-of-nonexpansive-semigroup-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111620180418On Brunn-Minkowski type inequality762769http://dx.doi.org/10.22436/jnsa.011.06.03ENLewen JiDepartment of Mathematics, East China University of Technology, Nanchang 330013, China \(\&\) Department of Mathematics, Shanghai University, Shanghai 200444, ChinaZhenbing ZengDepartment of Mathematics, East China University of Technology, Nanchang 330013, ChinaJingjing ZhongSchool of Public Finance and Public Administration, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaThe notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that
of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body. We also make some considerations for the polar of Orlicz combination.http://isr-publications.com/jnsa/7028/download-on-brunn-minkowski-type-inequalityInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111620180418Sharp generalized Papenfuss-Bach-type inequality770777http://dx.doi.org/10.22436/jnsa.011.06.04ENLing ZhuDepartment of Mathematics, Zhejiang Gongshang University, Hangzhou, ChinaIn this paper, we prove and develop a conjecture on the generalized double
Papenfuss-Bach inequality proposed by Sun and Zhu [Z. Sun, L. Zhu, J. Appl. Math., \(\textbf{2011}\) (2011), 9 pages]. In the last section
we pose a conjecture on a general form of Papenfuss-Bach-type inequality.http://isr-publications.com/jnsa/7029/download-sharp-generalized-papenfuss-bach-type-inequality