<abstract><p>Given a bounded open set $ \Omega\subseteq{\mathbb{R}}^n $, we consider the eigenvalue problem for nonlinear mixed local/nonlocal operator with vanishing conditions in complement of \Omega $. We prove that second \lambda_2(\Omega) is always strictly larger than first \lambda_1(B) ball B volume half This bound proven to be sharp, by comparing limit case which consists tw...

In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family J?(?,?,s,t,q;h) holomorphic bi-univalent functions which were defined in unit disk D associated with q-Srivastava–Attiya operator. We establish bounds for |a2| |a3|, where a2, a3 are initial Taylor–Maclaurin coefficients. For investigate Fekete-Szegö inequality, special cases consequences.

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp estimates the first four initial coefficients of this class are addressed. Furthermore, we obtain Fekete–Szegö inequality, sharp upper bounds second and third Hankel determinants, logarithmic coefficients, third-order determinants two...

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to involution numbers. find initial estimates Taylor–Maclaurin coefficients |a2| |a3| for functions introduced here. also obtain a Fekete–Szegö inequality class. Several consequences our results pointed out, not yet discussed as...

In the present paper, a subclass of analytic and biunivalent functions by means Gegenbauer polynomials is introduced. Certain coefficients bound for belonging to this are obtained. Furthermore, Fekete-Szegö problem solved. A number known or new results shown follow upon specializing parameters involved in our main results.

We defined two new subclasses of analytic bi-univalent function class Σ, in the open unit disk related with Sălăgean–Erdély–Kober operator. The bounds on initial coefficients |a2|,|a3| and |a4| for functions these Σ are investigated. Using estimates a2,a3, we also discuss Fekete-Szegö inequality results classes this paper. Relevant connections results, presented here as corollaries, not studied...

In current manuscript, using Laguerre polynomials and (p−q)-Wanas operator, we identify upper bounds a2 a3 which are first two Taylor-Maclaurin coefficients for a specific bi-univalent functions classes W∑(η,δ,λ,σ,θ,α,β,p,q;h) K∑(ξ,ρ,σ,θ,α,β,p,q;h) cover the convex starlike functions. Also, discuss Fekete-Szegö type inequality defined class.

In this paper, we define a subclass of analytic functions by denote $T_{\beta}H\left( z,C_{n}^{\left( \lambda \right) }\left( t\right) $ satisfying the following subordinate condition \begin{equation*} \left( 1-\beta \frac{zf^{^{\prime }}\left( z\right) }{f\left( }\right) +\beta 1+\frac{zf^{^{\prime \prime }{f^{^{\prime \prec \frac{1}{\left( 1-2tz+z^{2}\right) ^{\lambda }}, \end{equation*} wher...

This expository article shows how classical inequalities for the derivative of polynomials can be proved in real and complex Hilbert spaces using only elementary arguments from functional analysis. As we shall see, there is a surprising interconnection between an equality of norms for symmetric multilinear mappings due to Banach and an inequality for the derivative of trigonometric polynomials ...