Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2026 08 01 Maximal area integral problem for a family of multivalent functions of starlike type 1 15 10771 10.22075/ijnaa.2025.34134.5095 EN C Infantina Sharmi Department of Mathematics, Madras Christian College, Tambaram, Chennai-600059, Tamil Nadu, India 0009-0005-7790-3149 S Sunil Varma Department of Mathematics, Madras Christian College, Tambaram, Chennai-600059, Tamil Nadu, India 0000-0001-8780-3751 Journal Article 2024 05 14 For a normalized analytic multivalent function $f$ defined in the open unit disk $\{z \in \mathbb{C}:|z|<1\},$ let $\Delta(r,f)$ and $L(r,f,p)$ denote the Dirichlet integral and the integral mean of $f$, respectively. In this research article, we consider a subclass $S^{*}_{p}(A,B,\lambda)$ of normalized analytic multivalent functions in the open unit disk and solve the Yamashitha's conjecture for this subclass. Also, we determine the extremal function for which the integral mean $L(r,f,p)$ is maximum. multivalent analytic function subordination Integral means area integral Gaussian hypergeometric functions https://ijnaa.semnan.ac.ir/article_10771_85be7e92377849414323f55a9e3c4e36.pdf