http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
TURÁN-TYPE $L^r$-INEQUALITIES FOR POLAR DERIVATIVE OF A POLYNOMIAL
Robinson Soraisam,Mayanglambam Singhajit Singh,Barchand Chanam 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.3
In this paper, we obtain an improved extension of the above inequality into polar derivative. Further, we also extend an inequality on polar derivative recently proved by Rather et al. \cite{SLBEPD2021}into $L^{r}$-norm. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.
SOME INEQUALITIES ON POLAR DERIVATIVE OF A POLYNOMIAL
N. Reingachan,Robinson Soraisam,Barchand Chanam 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
In this paper, we establish some extensions and refinements of the above inequality topolar derivative and some other well-known inequalities concerning the polynomials and theirordinary derivatives.
N. Reingachan,Robinson Soraisam,Barchand Chanam 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
In this paper, we present some fixed point theorems for rational type contractiveconditions in the setting of a complete metric space via a cyclic (α, β)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.
INEQUALITIES FOR COMPLEX POLYNOMIAL WITH RESTRICTED ZEROS
Istayan Das,Robinson Soraisam,Mayanglambam Singhajit Singh,Nirmal Kumar Singha,Barchand Chanam 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
Let $p(z)$ be a polynomial of degree $n$ and for any complex number $\beta$, let $D_\beta p(z)=np(z)+(\beta-z)p^\prime(z)$ denote the polar derivative of the polynomial with respect to $\beta$. In this paper, we consider the class of polynomial$$p(z)=(z-z_{0})^s\left(a_{0}+\displaystyle{\sum_{\nu=0}^{n-s}a_{\nu}z^{\nu}}\right)$$ of degree $n$ having a zero of order $s$ at $z_0$, $|z_{0}|<1$ and the remaining $n-s$ zeros are outside $|z|<k$, $k\geq1$ and establish upper bound estimates for the maximum of $\left|D_\beta p(z)\right|$ as well as $\left|p(Rz)-p(rz)\right|$, $R\geq r\geq1$ on the unit disk.
IMPROVED VERSION ON SOME INEQUALITIES OF A POLYNOMIAL
Rashmi Rekha Sahoo,N. Reingachan,Robinson Soraisam,Khangembam Babina Devi,Barchand Chanam 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
Let $P(z)$ be a polynomial of degree $n$ and $P(z)\neq0$ in $|z|<1$. Then for every real $\alpha$ and $R>1$,Aziz \cite{Aziz1} proved that$$ \max_{|z|=1}|P(Rz)-P(z)|\leq \frac{R^{n}-1}{2}\left(M_{\alpha}^{2}+M_{\alpha+\pi}^{2}\right)^{\frac{1}{2}},$$where\begin{equation*}M_{\alpha}=\max_{1\leq k\leq n}|P(e^{i(\alpha+2k\pi) n})|. \end{equation*}\par In this paper, we establish some improvements and generalizations of the above inequality concerning the polynomials and their ordinary derivatives.
HIGHER DERIVATIVE VERSIONS ON THEOREMS OF S. BERNSTEIN
Thangjam Birkramjit Singh,Khangembam Babina Devi,N. Reingachan,Robinson Soraisam,Barchand Chanam 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2
In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.