Sabir Ahammed

Bohr's theorem for Cesáro operator and certain integral transforms over octonions

Molla Basir Ahamed, Sabir Ahammed

In this paper, we first establish the Bohr's theorem for Cesáro operator defined for $f \in S R B (B)$ of slice regular functions in the open unit ball $B$ …

Bohr phenomena for slice regular functions over Quaternions

Sabir Ahammed, Molla Basir Ahamed, Ming-Sheng Liu

Slice regular functions are a generalization of holomorphic functions to the setting of quaternions (and more generally, Clifford algebras). In this paper, we first establish the B…

The Bohr inequality for vector-valued holomorphic functions with lacunary series in complex Banach spaces

Sabir Ahammed, Molla Basir Ahamed, Rajesh Hossain

In this paper, we study the Bohr inequality with lacunary series for vector-valued holomorphic functions defined in unit ball of finite dimensional Banach sequence space. Also, we…

Improved and Refined Bohr-Type Inequalities for Slice Regular Functions over Octonions

Sabir Ahammed, Molla Basir Ahamed

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative se…

Schwarzian Norm Estimates for Analytic Functions Associated with Convex Functions

Molla Basir Ahamed, Rajesh Hossain, Sabir Ahammed

Let $A$ denote the class of analytic functions $f$ on the unit disc $D = {z \in C : ∣ z ∣ < 1}$ normalized by $f (0) = 0$ and $f^{'} (0) = 1$ . In the present a…

The Bohr radius for operator valued functions on simply connected domain

Sabir Ahammed, Molla Basir Ahamed

In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $Ω$ in $C$ . Next, we…

Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces

Molla Basir Ahamed, Sabir Ahammed, Hidetaka Hamada

In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_{X}$ of a complex Banach space $X$ into $\mat…

Bohr radius for invariant families of bounded analytic functions and certain Integral transforms

Molla Basir Ahamed, Partha Pratim Roy, Sabir Ahammed

In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $D$ . Then, we obtain Bohr inequality for certain i…

The Bohr inequality on a simply connected domain and its applications

Sabir Ahammed, Molla Basir Ahamed, Partha Pratim Roy

In this article, we first establish a generalized Bohr inequality and examine its sharpness for a class of analytic functions $f$ in a simply connected domain $Ω_{γ},$ where $0\leq γ…

Bohr-type inequalities for classes of analytic maps and K-quasiconformal harmonic mappings

Molla Basir Ahamed, Sabir Ahammed

In this paper, a significant improvement has been achieved in the classical Bohr's inequality for the class $B$ of analytic self maps defined on the unit disk $ \mathbb…

Bohr-Rogosinski inequalities involving Schwarz functions

Sabir Ahammed, Molla Basir Ahamed

In this paper, we study Bohr's inequality and refined versions of Bohr-Rogosinski inequalities involving Schwarz functions. Moreover, we establish a version of multidimensional ana…

Operator-valued analogues of multidimensional Bohr-Rogosinski inequalities

Sabir Ahammed, Molla Basir Ahamed

In this article, we first establish operator-valued analogues of multidimensional refined Bohr inequality. Then we establish operator-valued analogues of multidimensional improved…