Certain Classes of Analytic Functions Bound with Kober Operators in $q$-Calculus

Abstract

Through applying the Kober fractional q -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q -differintegral operator in the open disk U = ξ ∈ ℂ : ∣ ξ | < 1 . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed immediately. The findings include an expansion of the numerous established results in the q -theory of analytical functions.

Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

“…Here we also passing to remark that, many well-known authors have studied different subclasses of analytic and bi-univalent functions form different aspects. For example in univalent function theory in conjunction with q-calculus the works given in [29,36,37,53] are worth mentioning.…”