Special Sessions

SS-1: Appell Polynomials and Approximation Theory with Applications II (confirmed)

Organizers:

• Mehmet Ali Özarslan (Eastern Mediterranean University, mehmetali.ozarslan@emu.edu.tr)
• Bayram Çekim (Gazi University, bayramcekim@gazi.edu.tr)
• Mustafa Kara (Eastern Mediterranean University, mustafa.kara@emu.edu.tr)

Description: The aim of SS-1 is to bring together academics whose research topics are mainly focused on the Appell-type polynomials (Appell, Binomial, Sheffer, Boas–Buck polynomials, etc.), approximation theory, and their connections with applications. We welcome research papers, as well as review papers, covering, but not limited to, any of the following topics:

• General types of Appell polynomials with analytical properties and applications.
• Certain special cases of Appell (and/or special) polynomials and numbers (Bernoulli, Euler, Hermite, Charlier, Fibonacci, etc.).
• Approximation properties of linear, positive operators constructed based on general (and/or special cases of) Appell-type polynomials.
• Appell-type polynomials from the operational calculus point of view.
• Linear positive operators constructed based on certain special functions.

Contact: To participate in SS-1, please first contact the organizer(s) of the session via the email addresses above.

Note: This special session is a continuation of the session with the same title that was held at ATSF 2024, where 12 successful presentations were delivered (click here for details).

SS-2: Approximation by Nonlinear Operators and Their Applications II (confirmed)

Organizers:

• İsmail Aslan (Hacettepe University, ismail-aslan@hacettepe.edu.tr)
• Türkan Yeliz Gökçer Ellidokuz (Bahçeşehir University, ylzgkcr@gmail.com)

Description: The primary goal of SS-2 is to provide a high-level forum for researchers to present novel forms of nonlinear approximation operators and discuss the latest advancements in approximation theory. While classical linear operators provide a robust foundation, nonlinear approaches - including sublinear, pseudo-linear, max-product and max-min operators - have become indispensable for capturing complex behaviors in modern data science. This session aims to foster active discussions concerning efficient methodologies for achieving improved convergence rates and high-order approximation results. A key focus will be the bridge between abstract functional analysis and practical implementation. We particularly welcome contributions that carefully analyze the potential impact of these techniques across diverse application domains, such as digital image processing, signal filtering and reconstruction. The highlighted topics are as follows:

• Classical approximation, rates of convergence.
• Sampling operators and interpolation operators.
• Approximation by neural networks.
• Max-product operators and max-min operators.
• Nonlinear operators, pseudo-linear operators, sublinear operators.
• Summability on nonlinear operators.

Contact: To participate in SS-2, please first contact the organizer(s) of the session via the email addresses above.

SS-3: New Results in Time Scales Calculus (confirmed)

Organizer:

• Tom Cuchta (Marshall University, cuchta@marshall.edu)

Description: This session welcomes all speakers who work in time scales calculus and related fields. Time scales calculus serves to unify and extend continuous and discrete analysis into one theory. Some suggested topics may include:

• Special functions on time scales.
• How time scales calculus can improve numerical algorithms.
• New dynamic equations of all types.
• Novel operators, including fractional.
• New definitions that generalize a new concept to the time scales framework.
• Analysis of operators such as the Laplace transform.

Contact: To participate in SS-3, please first contact the organizer(s) of the session via the email address above.

SS-4: Advances in Special Functions-Based Approximation Theory for Mathematical Modeling in Engineering, Finance, and Applied Sciences (confirmed)

Organizers:

• Zakaria El Allali (Mohammed First University, Oujda, Morocco, z.elallali@ump.ac.ma)
• Faissal El Bouanani (Mohammed V University, Rabat, Morocco, f.elbouanani@um5s.net.ma)

Description: The special session SS-4 convenes at the confluence of special functions, approximation theory, and applied mathematics to address pressing challenges in engineering, finance and applied sciences. The accurate modeling of complex stochastic phenomena in these domains necessitates the use of highly flexible probability distributions, among which the Generalized Gamma (GG) distribution is preeminent for its ability to unify a wide range of statistical models, from Rayleigh and Nakagami-m to Weibull and Gamma. A core theme of this session is the exploration of advanced analytical and numerical techniques to handle these complex distributions. A significant challenge lies in the efficient and accurate approximation of their probability density functions (PDFs) and cumulative distribution functions (CDFs). This session will feature innovative work on the use of Fox's H-function as a powerful tool to approximate the sum, ratio, and product of generalized distributions, not necessarily identical neither uncorrelated. By leveraging methods such as Moment-based approaches, Cubic Spline interpolation, Saddle Point Approximation, and other numerical schemes, this approach provides a unified framework for performance analysis and risk assessment in diverse applications. The session will provide a high-level platform for sharing new research, fostering collaborations, and exploring future directions in the application of these sophisticated mathematical tools. The session will cover a wide range of topics, from the theoretical properties of special functions to their practical applications in engineering and finance. We welcome contributions that present new analytical techniques, numerical methods, and case studies. A key objective is to highlight the power of using integral transforms and higher transcendental functions, like Fox's H-function, to solve pressing real-world problems. The session will emphasize the interdisciplinary nature of the field and encourage the cross-fertilization of ideas between different areas of application. Topics of interest include, but are not limited to:

• Approximation of generalized distributions using Fox's H-Function, with applications to performance analysis in engineering systems and financial risk modeling.
• Advanced approximation techniques including saddle point methods, cubic spline interpolation, moment-based approaches, and asymptotic analysis for special functions in diverse applied contexts.
• Orthogonal polynomials and special functions in signal processing, image analysis, and control theory.
• Hypergeometric and confluent hypergeometric functions in the pricing of exotic financial derivatives, credit risk modeling, and asset allocation.
• Applications of q-calculus and fractional calculus in financial modeling and signal processing.
• Special functions in the modeling of stochastic processes (e.g., Lévy processes) in finance.

Contact: To participate in SS-4, please first contact the organizer(s) of the session via the email addresses above.