publications

Selected Publications

1. Gaba, Y.U., & Künzi, H.P.A. (2016). Partially ordered metric spaces produced by T₀-quasi-metrics. Topology and its Applications, 202, 366–383.
2. Gaba, Y.U. (2017). Fixed point theorems in G-metric spaces. Journal of Mathematical Analysis and Applications, 455(1), 528–537.
3. Gaba, Y.U., & Künzi, H.P.A. (2015). Splitting metrics by T₀-quasi-metrics. Topology and its Applications, 193, 84–96.
4. Gaba, Y.U., Karapınar, E., Petruşel, A., & Radenović, S. (2019). New results on start-points for multi-valued maps. Axioms, 9(4), 141.
5. Gaba, Y.U., Aphane, M., & Aydi, H. (2021). (α, b_k)-contractions in bipolar metric spaces. Journal of Mathematics, 2021.
6. Gaba, Y.U. (2017). Metric type spaces and λ-sequences. Quaestiones Mathematicae, 40(1), 49–55.
7. Agyingi, C.A., & Gaba, Y.U. (2019). Hyperconvexity in quasi-metric spaces. Afrika Matematika, 30, 399–412.
8. Gaba, Y.U., Aphane, M., & Sihag, V. (2021). On two Banach-type fixed points in bipolar metric spaces. Abstract and Applied Analysis, 2021.

View full publication list on ORCID

Top 5 arXiv Preprints

1. Gaba, Y.U. (2026). Expansive homeomorphisms on complexity quasi-metric spaces. arXiv:2602.07685
2. Iradukunda, M.D., Elégbédé, C.F., & Gaba, Y.U. (2026). Intelligent resource allocation in wireless networks via deep reinforcement learning. arXiv:2601.04842
3. Hounwanou, C.D., & Gaba, Y.U. (2025). Deep Generative Models for Synthetic Financial Data: Applications to Portfolio and Risk Modeling. arXiv:2512.21798
4. Hounwanou, C.D., Gaba, Y.U., & Ntakirutimana, P. (2025). Synthetic Financial Data Generation for Enhanced Financial Modelling. arXiv:2512.21791
5. Janardhanan, G., Mani, G., Kennedy, N.D.J., & Gaba, Y.U. (2025). On Fixed Point Theorems in Bipolar Metric Spaces Involving Polynomial-Type Contractions. arXiv:2508.05566

View all preprints on arXiv

Full Bibliography

2025

1. arXiv

   

   Bellman Operator Convergence Enhancements in Reinforcement Learning Algorithms

   David Krame Kadurha, Domini Jocema Leko Moutouo, and Yaé Ulrich Gaba

   2025

   Abs arXiv Bib

   This paper reviews the topological groundwork for the study of reinforcement learning by focusing on the structure of state, action, and policy spaces, and illustrates how the Banach fixed-point theorem explains the convergence of RL algorithms. Alternative Bellman operator formulations are explored and tested on standard environments including MountainCar, CartPole, and Acrobot.

   @article{kadurha2025bellman,
     title = {Bellman Operator Convergence Enhancements in Reinforcement Learning Algorithms},
     author = {Kadurha, David Krame and Moutouo, Domini Jocema Leko and Gaba, Ya{\'e} Ulrich},
     year = {2025},
     archiveprefix = {arXiv},
     primaryclass = {cs.LG},
   }

2024

1. Book

   

   The Shape of Data: Geometry-Based Machine Learning and Data Analysis in R

   Colleen M. Farrelly and Yaé Ulrich Gaba

   2024

   Abs Bib HTML

   A comprehensive guide to geometry-based machine learning and data analysis, covering topological data analysis, persistent homology, and geometric methods with practical implementations in R.

   @book{farrelly2024shape,
     title = {The Shape of Data: Geometry-Based Machine Learning and Data Analysis in {R}},
     author = {Farrelly, Colleen M. and Gaba, Ya{\'e} Ulrich},
     year = {2024},
     publisher = {No Starch Press},
     isbn = {9781718503083},
   }

2. arXiv

   

   Topological Foundations of Reinforcement Learning

   David Krame Kadurha and Yaé Ulrich Gaba

   2024

   Abs arXiv Bib

   This work serves as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. It connects the Banach fixed point theorem to RL algorithm convergence and demonstrates how mathematical insights from topology can inform more efficient RL algorithm design.

   @article{kadurha2024topological,
     title = {Topological Foundations of Reinforcement Learning},
     author = {Kadurha, David Krame and Gaba, Ya{\'e} Ulrich},
     year = {2024},
     archiveprefix = {arXiv},
     primaryclass = {cs.LG},
   }

3. DRL

   

   Intelligent Resource Allocation in Wireless Networks via Deep Reinforcement Learning

   Yaé Ulrich Gaba and others

   2024

   Abs Bib HTML

   This study addresses optimal power allocation in stochastic wireless networks by employing a Deep Reinforcement Learning framework, designing a Deep Q-Network agent capable of learning adaptive power control policies directly from channel state observations.

   @article{gaba2024wireless,
     title = {Intelligent Resource Allocation in Wireless Networks via Deep Reinforcement Learning},
     author = {Gaba, Ya{\'e} Ulrich and others},
     year = {2024},
   }

2022

1. JFS

   

   Existence and Uniqueness of Common Fixed Point on Complex Partial b-Metric Space

   Arul Joseph Gnanaprakasam, Yaé Ulrich Gaba, and others

   Journal of Function Spaces, 2022

   DOI Bib HTML

   @article{gaba2022complex,
     title = {Existence and Uniqueness of Common Fixed Point on Complex Partial $b$-Metric Space},
     author = {Gnanaprakasam, Arul Joseph and Gaba, Ya{\'e} Ulrich and others},
     journal = {Journal of Function Spaces},
     year = {2022},
     publisher = {Wiley},
     doi = {10.1155/2022/1925612},
   }

2021

1. JMath

   

   Interpolative Kannan Contractions in T_0-Quasi-Metric Spaces

   Yaé Ulrich Gaba and Erdal Karapınar

   Journal of Mathematics, 2021

   Abs DOI Bib HTML

   In this paper, the well-known fixed point theorem of Kannan is updated using the interpolation notion in the realm of quasi-metric spaces, considering some asymmetric versions.

   @article{gaba2021interpolative,
     title = {Interpolative Kannan Contractions in $T_0$-Quasi-Metric Spaces},
     author = {Gaba, Ya{\'e} Ulrich and Karap{\i}nar, Erdal},
     journal = {Journal of Mathematics},
     year = {2021},
     publisher = {Wiley},
     doi = {10.1155/2021/6685638},
   }

2. JMath

   

   (α, BK)-Contractions in Bipolar Metric Spaces

   Yaé Ulrich Gaba and others

   Journal of Mathematics, 2021

   Abs DOI Bib HTML

   Introduction of (α, BK)-contractions and proof of existence of fixed points for contravariant mappings on bipolar metric spaces.

   @article{gaba2021bipolar,
     title = {($\alpha$, BK)-Contractions in Bipolar Metric Spaces},
     author = {Gaba, Ya{\'e} Ulrich and others},
     journal = {Journal of Mathematics},
     year = {2021},
     publisher = {Wiley},
     doi = {10.1155/2021/5562651},
   }

2020

1. Axioms

   

   New Results on Start-Points for Multi-Valued Maps

   Yaé Ulrich Gaba, Erdal Karapınar, Adrian Petruşel, and 1 more author

   Axioms, 2020

   Abs DOI Bib HTML

   This manuscript investigates the existence of start-points for generalized weakly contractive multi-valued mappings in the setting of left K-complete quasi-pseudo metric space.

   @article{gaba2020startpoints,
     title = {New Results on Start-Points for Multi-Valued Maps},
     author = {Gaba, Ya{\'e} Ulrich and Karap{\i}nar, Erdal and Petru{\c{s}}el, Adrian and Radeno\-vi{\'c}, Stojan},
     journal = {Axioms},
     volume = {9},
     number = {4},
     pages = {141},
     year = {2020},
     publisher = {MDPI},
     doi = {10.3390/axioms9040141},
   }

2019

1. arXiv

   

   Quasi-uniform Type Spaces

   Yaé Ulrich Gaba

   2019

   Abs arXiv Bib

   We introduce the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that topological and quasi-uniformity theories applicable to quasi-metric spaces extend to these generalized spaces, and prove that the Banach, Kannan, Reich and Chatterjea fixed point theorems can be successfully extended to this more general setting.

   @article{gaba2019quasiuniform,
     title = {Quasi-uniform Type Spaces},
     author = {Gaba, Ya{\'e} Ulrich},
     year = {2019},
     archiveprefix = {arXiv},
     primaryclass = {math.GN},
   }

2. Axioms

   

   A New Approach to the Interpolative Contractions

   Yaé Ulrich Gaba and Erdal Karapınar

   Axioms, 2019

   Abs DOI Bib HTML

   A new approach to interpolative contractions in the framework of quasi-metric spaces.

   @article{gaba2019interpolative,
     title = {A New Approach to the Interpolative Contractions},
     author = {Gaba, Ya{\'e} Ulrich and Karap{\i}nar, Erdal},
     journal = {Axioms},
     volume = {8},
     number = {4},
     pages = {110},
     year = {2019},
     publisher = {MDPI},
     doi = {10.3390/axioms8040110},
   }

3. ACDM

   

   New Fixed Point Results in Quasi-Metric Spaces and Applications in Fractals Theory

   Yaé Ulrich Gaba and others

   Advances in Continuous and Discrete Models, 2019

   DOI Bib HTML

   @article{gaba2019fixedpoint,
     title = {New Fixed Point Results in Quasi-Metric Spaces and Applications in Fractals Theory},
     author = {Gaba, Ya{\'e} Ulrich and others},
     journal = {Advances in Continuous and Discrete Models},
     year = {2019},
     publisher = {Springer},
     doi = {10.1186/s13662-019-2119-z},
   }

2017

1. arXiv

   

   η-Metric Structures

   Yaé Ulrich Gaba

   2017

   Abs arXiv Bib

   We introduce the notion of η-cone metric spaces and explore their topological properties, proving fixed point theorems for contractive type maps on these spaces. These structures generalize both cone metric spaces and metric type spaces.

   @article{gaba2017eta,
     title = {$\eta$-Metric Structures},
     author = {Gaba, Ya{\'e} Ulrich},
     year = {2017},
     archiveprefix = {arXiv},
     primaryclass = {math.GN},
   }

2. FPTA

   

   New Contractive Conditions for Maps in d-Generalized Metric Spaces

   Yaé Ulrich Gaba

   Fixed Point Theory and Applications, 2017

   Bib

   @article{gaba2017newcontractions,
     title = {New Contractive Conditions for Maps in $d$-Generalized Metric Spaces},
     author = {Gaba, Ya{\'e} Ulrich},
     journal = {Fixed Point Theory and Applications},
     year = {2017},
     publisher = {Springer},
   }

3. JA

   

   Common Fixed Points in Generalized Quasi-Metric Spaces

   Yaé Ulrich Gaba

   Journal of Analysis, 2017

   Bib

   @article{gaba2017common,
     title = {Common Fixed Points in Generalized Quasi-Metric Spaces},
     author = {Gaba, Ya{\'e} Ulrich},
     journal = {Journal of Analysis},
     year = {2017},
   }

2016

1. PhD

   

   Construction of Quasi-Metrics Determined by Orders

   Yaé Ulrich Gaba

   University of Cape Town, 2016

   Abs Bib HTML

   PhD thesis in Topology, investigating the construction of quasi-metrics from ordered structures with applications to fixed point theory.

   @phdthesis{gaba2016thesis,
     title = {Construction of Quasi-Metrics Determined by Orders},
     author = {Gaba, Ya{\'e} Ulrich},
     year = {2016},
     school = {University of Cape Town},
   }

2015

1. AMat

   

   Fixed Points on Partial Metric Type Spaces

   Yaé Ulrich Gaba

   Afrika Matematika, 2015

   Bib

   @article{gaba2015fixedpartial,
     title = {Fixed Points on Partial Metric Type Spaces},
     author = {Gaba, Ya{\'e} Ulrich},
     journal = {Afrika Matematika},
     year = {2015},
     publisher = {Springer},
   }

2014

1. JMath

   

   Startpoints and (α, γ)-Contractions in Quasi-Pseudometric Spaces

   Yaé Ulrich Gaba

   Journal of Mathematics, 2014

   Abs DOI Bib HTML

   Introduces the concept of startpoint and endpoint for multivalued maps defined on a quasi-pseudometric space and investigates the relation between these new concepts and the existence of fixed points.

   @article{gaba2014startpoints,
     title = {Startpoints and ($\alpha$, $\gamma$)-Contractions in Quasi-Pseudometric Spaces},
     author = {Gaba, Ya{\'e} Ulrich},
     journal = {Journal of Mathematics},
     year = {2014},
     publisher = {Wiley/Hindawi},
     doi = {10.1155/2014/709253},
   }

2. AMat

   

   Fixed Point Theorems in Generalized Quasi-Metric Spaces

   Yaé Ulrich Gaba

   Afrika Matematika, 2014

   Bib

   @article{gaba2014fixed,
     title = {Fixed Point Theorems in Generalized Quasi-Metric Spaces},
     author = {Gaba, Ya{\'e} Ulrich},
     journal = {Afrika Matematika},
     year = {2014},
     publisher = {Springer},
   }

3. arXiv

   

   An Order Theoretic Approach in Fixed Point Theory

   Yaé Ulrich Gaba

   2014

   arXiv Bib

   @article{gaba2014order,
     title = {An Order Theoretic Approach in Fixed Point Theory},
     author = {Gaba, Ya{\'e} Ulrich},
     year = {2014},
     archiveprefix = {arXiv},
   }