Sharp coefficient inequalities for a class of analytic functions defined by q-difference operator associated with q-Lemniscate of Bernoulli


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Authors

  • Mohammad Faisal Khan Department of Basic sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
  • Shahid Khanl Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan
  • Maslina Darus Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia
  • Saqib Hussain Department of Mathematics, COMSATS University Islamabad, Abbottabad, Campus, 22060 Abbottabad, Pakistan

Keywords:

Analytic functions, q-Differential operator, Hankel determinant, q-Starlike functions, Ruscheweyh q-differential operator, q-Lemniscate of Bernoulli

Abstract

Quantum theory has many applications in mathematics, particularly in the study of special functions and quantum physics. In this article, based on the concept of Lemniscate of Bernoulli, we provide q-Lemniscate of Bernoulli (x2 +y2) -2(x2 - y2) = q2 - 1. The q-Lemniscate Bernoulli is used to define a new class of analytic functions using a quantum di¤erence operator, and for this class,
an upper bound Fekete-Szegö problems and the second Hankel determinant are studied. Furthermore, several known cases with proven findings are presented. In addition, by using the Ruscheweyh q-di¤erential operator, certain useful applications of the main findings are attained.

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Published

2023-10-20

How to Cite

Mohammad Faisal Khan, Shahid Khanl, Maslina Darus, & Saqib Hussain. (2023). Sharp coefficient inequalities for a class of analytic functions defined by q-difference operator associated with q-Lemniscate of Bernoulli. Results in Nonlinear Analysis, 6(4), 55–73. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/272

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