In this paper, we introduce new formulation of the BA transform associated with fractional integral operators whose kernels incorporate the generalized S-function within a unified parametric framework. The proposed approach generalizes existing fractional integral models and establishes a more flexible analytical structure by accommodating a broad class of parameters. By employing pathway fractional operators, we derive several key results that yield new identities and deeper insights into the theory of integral transforms. The effectiveness of the proposed BA transform, when combined with pathway fractional integrals featuring the generalized S-function kernel, is demonstrated, thereby contributing significantly to the advancement of generalized fractional calculus and its practical applications.
The purpose of the present paper is to extend the study of Reinhardt domains from ℂ^n to toric varieties. The main result clarifies pseudoconvexity and envelopes of holomorphy for subdomains of simplicial affine toric varieties. In conclusion, suggestions and open questions on the general case and related extension problems on toric varieties are discussed. The article is reasonably self-contained in order to make the material accessible to complex analysts.
The well-known concept of subordination between two analytic functions is referred to as weak subordination in the harmonic case, due to certain limitations. Let 𝔻 denote the open unit disk centered at the origin in the complex plane ℂ . In this article, a family of convex and univalent harmonic mappings, ℱ_β:𝔻→ℂ,β∈ℕ, is constructed using harmonic Alexander operator, and mapping properties of members of this family are discussed. It is established that the sequence {ℱ_β :β∈ℕ} forms a weak subordination chain.
We give the first main theorem and the second main theorem of Nevanlinna theory for meromorphic functions on complete Kähler manifolds which admit Green’s functions regular at infinity. Our method is applicable also for the cases when the domain manifolds of meromorphic functions are strictly pseudo-convex domains and bounded regular domains in complex Euclidean spaces.
Growth properties of entire function solutions of certain homogeneous partial differential equations have been discussed by various authors. The growth estimates of entire/analytic function solutions of non-homogenous partial differential equations have not been studied so far. Therefore, in this paper, we tried to bridge this gap. Moreover, the classical order, lower order, and type of entire function solutions of non-homogeneous partial differential equations of generalized axially symmetric potential theory in terms of coefficients occurring in its power series expansion in two complex variables have been obtained.
