Research

My Research Interest is Fixed Point Theory and Best Proximity Point Analysis

My ORCID is 0000-0001-6912-4712

Research Students

• S. Jamal Fathima (2018), Thesis Title : Studies on Fixed Point Theorems and Best Proximity Point Theorems 
• T. Piramatchi (2020), Thesis Title : A Study on the Existence of Best Proximity Points
• S. Gomathi (2021), Thesis Title : On Some Best Proximity Point Points
• K. Anisha (2025), Thesis Title : Best Proximity Point Theorems for Single and Multivalued Mappings ( Submitted )
• P. Periasamy (Jointly with Dr. K. Annathurai, Tiruvalluvar College) ( Ongoing )

 

Publications

• Sankar Raj Vaithilingam and K. Anisha, A Common Best Proximity Point Theorem for Relatively Nonexpansive Mappings, J. Analysis (2025) ( Accepted )

• Sankar Raj Vaithilingam  and K. Anisha, Best Proximity Point Theorems for Maia-Type Contraction Mappings, Electronic Journal of Mathematical Analysis and its Applications, Vol. 12(2), 2024, No.11

• V. Sankar Raj  and S. Gomathi, A best proximity point theorem for relatively nonexpansive mappings in the absence of the proximal normal structure property, Fixed Point Theory, Vol. 25, 2024, 333 - 338

• Sankar Raj Vaithilingam  and A. Dhanalakshmi, An Elementary Best Proximity Point Theorem in Metric Spaces, J. Analysis, Vol. 31, 2023, 1657 - 1664.

• V. Sankar Raj  and T. Piramatchi, Best Proximity Point Theorems in Topological Spaces, Journal of Fixed Point Theory and Applications, 2020, Vol. 22, Article 2 

• V. Sankar Raj  and T. Piramatchi, Two Extensions of Diametrically Contractive Mappings, Numerical Functional Analysis and Optimization, Vol. 41 ( 2020 ) pp. 432 -- 441.

• T. Piramatchi, S. Jamal Fathima and V. Sankar Raj, Strong Convergence of Approximants to Best Proximity Points of Nonself Nonexpansive Mappings, J. Analysis, Vol. 20 ( 2020 ) pp. 377 -- 385. 

• V. Sankar Raj and S. Jamal Fathima, On Park’s f-Contractive Cyclic Mappings, Journal of Nonlinear Analysis and Applications,  Vol. 2018, Issue 2 (2018) 145 --150. 

• V. Sankar Raj and S. Jamal Fathima, A Fixed Point Theorem for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Banach Spaces, J. Analysis,  Vol. 26, Issue 1 (2018), 09 -- 14.

• V. Sankar Raj and S. Jamal Fathima, Edelstein's Theorem for Non-self Multivalued Contractive Mappings, International Journal of Pure and Applied Mathematics,   Vol. 117, No.3 (2017) 375-382 

• V. Sankar Raj and A. Anthony Eldred, A Characterization of Strictly Convex Spaces and Applications, J. Optim. Theory Appl.,  Vol. 160, Issue 2(2014) pp. 703—710. 

• V. Sankar Raj, Best Proximity Point Theorems for Non-self Mappings, Fixed Point Theory,   Vol.14 No. 2 ( 2013 ) pp. 447—454.

• V. Sankar Raj and S. Somasundaram, KKM Type Theorems for Best Proximity Points,  Applied Mathematics Letters,   Vol.25 ( 2012 ) pp. 496—499.  

• V. Sankar Raj, A  Best Proximity Point Theorem for Weakly Contractive Non-self Mappings, Nonlinear Analysis : Theory, Methods & Applications,   Vol. 74 ( 2011 ) pp. 4804—4808. 

• A. Anthony Eldred, V. Sankar Raj and P. Veeramani, On Best Proximity Pair Theorems for Relatively u-Continuous Mappings, Nonlinear Analysis : Theory, Methods & Applications,   Vol. 74 ( 2011 ) pp. 3870—3875.

• A. Anthony Eldred, V. Sankar Raj, On Common Best Proximity Pair Theorems, Acta Sci. Math. (Szeged),   Vol. 75 ( 2009 ) pp. 707 — 721.  

• V. Sankar Raj and P. Veeramani, Best Proximity Point Theorems for Relatively Nonexpansive Mappings, Applied General Topology, Vol. 10 ( 2009 ) pp. 21 — 28. 

• V. Sankar Raj and P. Veeramani, A Fixed Point Theorem for Sum of Two Nonlinear Operators, Acta Sci. Math. (Szeged), Vol. 74 ( 2008 ) pp. 885 — 899.