arXiv subjects

Navneet Lal Sharma

Publications and source records attributed to Navneet Lal Sharma.

3 recordsLinked to original sources

arXiv2022

A correct proof of logarithmic coefficients for Janowski type $(j,k)$-symmetric starlike functions

Recently, authors [7] studied the logarithmic coefficient bounds for class of the Janowski type $(j,k)$-symmetric starlike functions $\mathcal{ST}_{[j,k]}(A,B)$ in ({\em Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.} (2022). DOI: 10.1007/s13398-022-01310-9). We pointed out that the proof of Theorem~3 in [7] is incorrect. In this article, we present the correct proof of Theorem~3. In addition, we also obtain some new results related to the logarithmic coefficient inequalities for the class $\mathcal{ST}_{[j,k]}(A,B)$.

math.CV↗

arXiv2014

Maximal area integral problem for certain class of univalent analytic functions

One of the classical problems concerns the class of analytic functions $f$ on the open unit disk $|z|<1$ which have finite Dirichlet integral $Δ(1,f)$, where $$Δ(r,f)=\iint_{|z|<r}|f'(z)|^2 \, dxdy \quad (0<r\leq 1). $$ The class ${\mathcal S}^*(A,B)$ of normalized functions $f$ analytic in $|z|<1$ and satisfies the subordination condition $zf'(z)/f(z)\prec (1+Az)/(1+Bz)$ in $|z|<1$ and for some $-1\leq B\leq 0$, $A\in {\mathbb C}$ with $A\neq B$, has been studied extensively. In this paper, we solve the extremal problem of determining the value of $$\max_{f\in {\mathcal S}^*(A,B)}Δ(r,z/f)$$ as a function of $r$. This settles the question raised by Ponnusamy and Wirths in [11]. One of the particular cases includes solution to a conjecture of Yamashita which was settled recently by Obradović et. al [9].

math.CV↗

arXiv2014

A note on a class of $p$-valent starlike functions of order beta

In this paper we obtain sharp coefficient bounds for certain $p$-valent starlike functions of order $β$, $0\le β<1$. Initially this problem was handled by Aouf in "M. K. Aouf, On a class of $p$-valent starlike functions of order $α$, Internat. J. Math. $\&$ Math. Sci. 1987;10:733--744". We pointed out that the proof given by Aouf was incorrect and a correct proof is presented in this paper.

math.CV↗