Initial Lucas polynomial coefficient bounds for bi-Bazilevi\v{c} functions

Altınkaya, Şahsene; Tejas, Nagamangala Sathyananda; Raju, Dasanur Shivanna; Magesh, Nanjundan

doi:10.22080/cjms.2024.27503.1702

Initial Lucas polynomial coefficient bounds for bi-Bazilevi\v{c} functions

Document Type : Research Articles

Authors

¹ uludag university

² Department of Mathematics, The National Institute of Engineering, Mysore - 570018, India

³ Visvesvaraya Technological University, Belagavi - 590018, India

⁴ 1Post-Graduate and Research Department of Mathematics, Government Arts College for Men Krishnagiri 635001, Tamilnadu, India.

10.22080/cjms.2024.27503.1702

Abstract

Our current investigation is primarily motivated by the application of special polynomials in Geometric Function Theory (GFT). This paper aims to utilize (M,N)-Lucas polynomials to estimate the initial coefficient bounds for a subclass of bi-univalent functions consisting of normalized analytic functions. We then derive the famous Fekete-Szegö inequality estimate. We also establish connections between our results and those examined in previous investigations.

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