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Mathematics
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New Advances in Complex Analysis and Functional Analysis
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New Advances in Complex Analysis and Functional Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C4: Complex Analysis".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1670

Special Issue Editor

Dr. Stanisława Kanas

E-Mail Website
Guest Editor
Institute of Mathematics, Uniwersytet Rzeszowski, al. Rejtana 16c, 35-959 Rzeszów, Poland
Interests: geometric function theory; differential subordinations; special functions; differential and integral operators; planar harmonic and quasiconformal mappings; entire and meromorphic function
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, “New Advances in Complex Analysis and Functional Analysis”, is devoted to the publication of high-quality research, especially that relating to geometrical aspects and harmonic as well as quasiconformal mappings, pure mathematical tools in functional analysis and applications (including applications in allied areas of mathematics and mathematical sciences). It will provide a forum for researchers and scientists to communicate their recent developments and present recent results in the theory of complex analysis of one and several variables, in addition to applications in algebraic geometry, number theory, and physics, including the branches of hydrodynamics and quantum mechanics.

The research topics include, but are not limited to, the following:

  • Complex analysis and potential theory.
  • Partial differential equations.
  • Geometrical aspects of complex analysis.
  • Complex approximation theory.
  • Harmonic and quasiconformal mappings.
  • Generalized complex analysis.
  • Complex dynamical systems and fractals.
  • Entire and meromorphic functions.
  • Functional equations.
  • Geometry of Banach spaces.
  • Linear operators.
  • Topological vector spaces.
  • Applications.

Dr. Stanisława Kanas
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • harmonic and quasiconformal mappings
  • entire and meromorphic functions
  • univalent and multivalent functions
  • subordinations and complex operator theory
  • geometrical aspects of complex analysis
  • special functions
  • applications of symmetry in mathematical analysis

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Published Papers (3 papers)

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Research

21 pages, 394 KB  
Article
Geometric Properties of Infinite Direct Sums
by Paweł Kolwicz
Mathematics 2026, 14(5), 906; https://doi.org/10.3390/math14050906 - 7 Mar 2026
Viewed by 356
Abstract
We show exactly when the topology of convergence in measure in Banach ideal spaces is linear (equivalently, coarser than the norm topology). Next, we present the relationship between the Kadets–Klee and suitable monotonicity properties with respect to global convergence in measure. Applying these [...] Read more.
We show exactly when the topology of convergence in measure in Banach ideal spaces is linear (equivalently, coarser than the norm topology). Next, we present the relationship between the Kadets–Klee and suitable monotonicity properties with respect to global convergence in measure. Applying these results, we characterize the Kadets–Klee property with respect to the global convergence in measure in infinite direct sums. We also prove the criteria of some related monotonicity properties in infinite direct sums. Furthermore, we solve the fundamental lifting (inheritance) problem completely for all these properties. We finish the paper with concrete examples showing how our general results can be applied. Full article
(This article belongs to the Special Issue New Advances in Complex Analysis and Functional Analysis)
18 pages, 636 KB  
Article
Directional Quaternion Step Differentiation and a Bicomplex Double-Step Calculus for Cancellation-Free First and Second Derivatives
by Ji Eun Kim
Mathematics 2026, 14(4), 728; https://doi.org/10.3390/math14040728 - 20 Feb 2026
Viewed by 350
Abstract
Accurate derivative information is central to sensitivity analysis and optimization, yet standard finite differences can lose many digits when the step size is small because of subtractive cancellation. Complex-step differentiation largely resolves this issue for first derivatives, but robust second derivatives and mixed [...] Read more.
Accurate derivative information is central to sensitivity analysis and optimization, yet standard finite differences can lose many digits when the step size is small because of subtractive cancellation. Complex-step differentiation largely resolves this issue for first derivatives, but robust second derivatives and mixed partials remain delicate: several practical complex-step variants for f″ still subtract nearly equal quantities, and quaternion-step rules are often presented as separate constructions. We develop a unified slice-based framework that extracts first and second derivatives from a single evaluation by projecting algebraic coefficients in commutative subalgebras of the complexified quaternions. First, we formulate a directional quaternion-steprule parameterized by an arbitrary unit pure quaternion u and provide an explicit projection operator that makes the underlying complex slice Cu≃C transparent; the resulting first-derivative formula is rotation invariant and recovers classical j-step and planar (j,k)-step rules as special cases. Second, we construct a bicomplex double-step calculus in the commuting imaginary units i and u and show that one evaluation at z+(i+u)h separates derivative information into distinct coefficients, with the iu-component equal to h2f″(z)+O(h4), giving a subtraction-free O(h2) approximation of f″. For bivariate analytic functions we additionally derive one-shot identities for fx, fy, and fxy from f(x+uh,y+ih) and supply practical extraction identities, step-size guidance for h2-scaled coefficients, and branch-consistency diagnostics for non-entire functions. The “cancellation-free” property here refers to avoiding the subtraction of nearly equal real quantities at the level of the differentiation formula; in floating-point arithmetic, coefficient extraction and the 1/h2 scaling for second-order quantities still interact with roundoff, and we quantify the resulting stable regimes numerically. Full article
(This article belongs to the Special Issue New Advances in Complex Analysis and Functional Analysis)
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12 pages, 299 KB  
Article
The Fekete–Szegö Inequality for a Certain Subclass of Analytic Functions of Complex Order Related to the q-Srivastava–Attiya Operator
by Dina Nabil, Matthew Olanrewaju Oluwayemi, Awatef Shahin and Hanan Darwish
Mathematics 2026, 14(4), 695; https://doi.org/10.3390/math14040695 - 16 Feb 2026
Viewed by 403
Abstract
The use of integral and differential operators in geometric function theory has continued to gain interest among researchers in the field of study in recent times. This is due to the wide range of its applications in science, technology and engineering. In this [...] Read more.
The use of integral and differential operators in geometric function theory has continued to gain interest among researchers in the field of study in recent times. This is due to the wide range of its applications in science, technology and engineering. In this work, therefore, the authors defined and investigated a new subclass of analytic functions in the open unit disk using the q-Srivastava–Attiya convolution operator and the Jackson’s q-derivative, by means of the subordination. The authors used two well-known lemmas to determine a sharp upper-bound for the Fekete–Szego¨ functional in two different cases. In particular, the authors introduced a new generalized subclass of complex order univalent functions denoted by Lq,b,hsτ,Φ and derived the coefficient estimates aι(ι=2,3) of the Taylor–Maclaurin series in this class, as well as the Fekete–Szego¨ inequality a3−ℵa22 for functions in this class. The work generalizes many known results in the literature. Full article
(This article belongs to the Special Issue New Advances in Complex Analysis and Functional Analysis)
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