In this paper, we prove an isoperimetric inequality for lower order eigenvalues of the free membrane problem on bounded domains in a Euclidean space or hyperbolic which strengthens well-known Szegö–Weinberger and supports celebrated conjecture Ashbaugh–Benguria.

The Schwarz rearrangement of u is denoted here by u. Inequality (1.1) has numerous applications in physics. It was first used in 1945 by G. Polya and G. Szegö to prove that the capacity of a condenser diminishes or remains unchanged by applying the process of Schwarz symmetrization (see [30]). Inequality (1.1) was also the key ingredients to show that, among all bounded bodies with fixed measur...

A class of p-valent analytic functions is introduced using the q-difference operator and familiar Janowski functions. Several properties in class, such as Fekete–Szegö inequality, coefficient estimates, necessary sufficient conditions, distortion growth theorems, radii convexity starlikeness, closure theorems partial sums, are discussed this paper.

In the present paper, we aimed to discuss certain coefficient-related problems for inverse functions associated with a bounded turning class subordinated exponential function. We calculated bounds of some initial coefficients, Fekete–Szegö-type inequality, and estimation Hankel determinants second third order. All these were proven be sharp.

Motivated by q-calculus, we define a new family of Σ, which is the bi-univalent analytic functions in open unit disc U that related to Einstein function E(z). We establish estimates for first two Taylor–Maclaurin coefficients |a2|, |a3|, and Fekete–Szegö inequality a3−μa22 belong these families.

In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′(z) (1− λ)f(z) + λzf ′(z) (0 ≤ λ < 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are giv...

We prove several isoperimetric inequalities for the conformal radius (or equivalently for the Poincaré density) of polygons on the hyperbolic plane. Our results include, as limit cases, the isoperimetric inequality for the conformal radius of Euclidean n-gons conjectured by G. Pólya and G. Szegö in 1951 and a similar inequality for the hyperbolic n-gons of the maximal hyperbolic area conjecture...

In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for analytic bi-univalent function class, which call Mocanu type bi-starlike functions, related to a shell-shaped region in open unit disk complex plane. Some interesting special cases of results are also discussed.

In the present article, using subordination principle, authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect symmetric and conjugate points. particular, bi-univalent conditions for function f(z) belonging these their relevant connections famous Fekete-Szegö inequality |a3−va22| were investigated a succinct mathematical approach.