Koşmaz Sünnetci, Betül; Bingöl, Özkan; Gedikli, Eyüp; Ekinci, Murat; Doğan, Ramazan Özgür; Türk, Salih; Güngör, Nihan

Featured Application: The proposed framework facilitates secure and user-friendly biometric authentication on mobile platforms, particularly in mobile payment and access control scenarios, under unconstrained conditions. The widespread adoption of mobile devices has made secure and user-friendly biometric authentication critical. However, widely used modalities such as fingerprint and facial recognition show limited robustness under uncontrolled illumination and on heterogeneous devices. In contrast, palmprint recognition offers strong potential because of its rich textural patterns and high discriminative power. This study addresses the limitations of laboratory-based datasets that fail to capture real-world challenges. We introduce MPW-180, a novel dataset comprising videos of 180 participants recorded on their own smartphones in everyday environments. By systematically incorporating diverse illumination conditions (with and without flash) and natural free-hand movements, MPW-180 is the first dataset to adopt a bring-your-own-device paradigm, providing a realistic benchmark for evaluating generalization in mobile biometric models. In addition, we propose PalmWildNet, an SE-block-enhanced deep learning architecture trained with Triplet Loss and a cross-illumination sampling strategy. The experimental results show that conventional methods suffer over 50% performance degradation under cross-illumination conditions. In contrast, our method reduces the Equal Error Rate to 1–2% while maintaining an accuracy above 97%. These findings demonstrate that the proposed framework not only tolerates illumination variability but also learns robust illumination-invariant representations, making it well-suited for mobile biometric authentication.

Gungor, Nihan; Dinc, Nagihan

A novel version of the Sumudu transform is introduced by using the notion of ∗-integral, which is called non-Newtonian Sumudu transform. The fundamental characteristics of the non-Newtonian Sumudu transform are demonstrated. The obtained results are applied to the solving of non-Newtonian differential equations and growth models.

Güngör, Nihan

Integral transforms have become the focus of investigations, because they allow the solution of significant problems in the domains of science and engineering to be accomplished with a minimal number of straightforward calculations. In this study, growth and decay problems, which are crucial in fields such as biology, zoology, physics, chemistry, and economics, are solved utilizing the Formable transform. The Formable transform method is applied to the logistic growth model in population and prey-predator models. The effectiveness and simplicity of the use of the Formable transform in obtaining the solution to these problems are examples.

Güngör, N.

In this study, we center upon obtaining the solution of linear bigeometric Volterra integral equations of the second kind in the sense of bigeometric calculus. The method of successive substitutions and resolvent kernel method are applied for solving the linear bigeometric Volterra integral equations of the second kind by using the concept of bigeometric integral. The necessary conditions for the bigeometric continuity and the uniqueness of the solution of linear bigeometric Volterra integral equations of the second kind are given in these methods. Finally, some numerical examples are presented to explain the procedure of the method of successive substitutions and resolvent kernel method.

Güngör, Nihan

Unfortunately, some of the corrections were missed in the original version and the corrections are as follows: In Theorem 1, the highlighted text should be in italics Let (Formula presented.) be (Formula presented.) continuous. Then, the following statements hold: (1) (Formula presented.) for all (Formula presented.) ,(2) (Formula presented.) for any (Formula presented.) ,(3)If (Formula presented.) for all (Formula presented.) , then (Formula presented.) ,(4)The functionfis (Formula presented.) bounded on (Formula presented.) ,(5) (Formula presented.) [10, 15]. (Formula presented.) for all (Formula presented.) , (Formula presented.) for any (Formula presented.) , If (Formula presented.) for all (Formula presented.) , then (Formula presented.) , The functionfis (Formula presented.) bounded on (Formula presented.) , (Formula presented.) [10, 15]. For (Formula presented.) , let (Formula presented.). Take f be a function with arguments in A and values in B, and let (Formula presented.). Then the following relations occur: In Theorem 9, the highlighted text should be in italics Suppose that the following conditions are satisfied:(i)f is (Formula presented.) continuous on (Formula presented.) ,(ii) (Formula presented.) is (Formula presented.) continuous on (Formula presented.) and (Formula presented.). f is (Formula presented.) continuous on (Formula presented.) , (Formula presented.) is (Formula presented.) continuous on (Formula presented.) and (Formula presented.). The Original Article was corrected.

Güngör, N.

In this study, we center upon obtaining the solution of linear bigeometric Volterra integral equations of the second kind in the sense of bigeometric calculus. The method of successive substitutions and resolvent kernel method are applied for solving the linear bigeometric Volterra integral equations of the second kind by using the concept of bigeometric integral. The necessary conditions for the bigeometric continuity and the uniqueness of the solution of linear bigeometric Volterra integral equations of the second kind are given in these methods. Finally, some numerical examples are presented to explain the procedure of the method of successive substitutions and resolvent kernel method

Güngör, Nihan

In this study, the Volterra integral equations are defined in the non-Newtonian calculus with the aid of ∗ -integral. The focus of this study is obtaining the solution of linear non-Newtonian integral equations. The ∗ -resolvent kernel method, successive approximations method and Adomian decomposition method are applied for solving non-Newtonian integral equations in the non-Newtonian sense. Some numerical examples are presented to explain the procedure of these methods. Finally, a model that describes a type of the exponential growth model is proposed in the sense of non-Newtonian calculus as an example.

Güngör, Nihan

In this study, the successive approximations method has been applied to investigate the solution for the linear bigeometric Volterra integral equations of the second kind in the sense of bigeometric calculus. The conditions to be taken into consideration for the bigeometric continuity and the uniqueness of the solution of linear bigeometric Volterra integral equations of the second kind are researched. Finally, some numerical examples are presented to illustrate successive approximations method.

Güngör, Nihan

Bu çalışmada, bigeometrik integral yardımıyla bigeometrik Volterra integral denklemleri tanımlanmıştır. Çalışmanın asıl amacı bigeometrik manada Volterra integral denklemleri ile bigeometrik manada diferansiyel denklemler arasındaki ilişkiyi araştırmaktır.

Güngör, Nihan

In this paper, we generalize the concepts of convexity, strict convexity and uniform convexity in the sense of non-Newtonian calculus. The main aim of this study is to obtain the non-Newtonian convexity, non-Newtonian strict convexity and non-Newtonian uniform convexity properties of the non-Newtonian sequence spaces lp(N).