Prowadzę badania w zakresie teorii punktu stałego i analizy nieliniowej.

1. A. Nowakowski, R. Plebaniak, Fixed point theorems and periodic problems for nonlinear Hill’s equation, Nonlinear Differ. Equ. Appl. (2023) 30:16,https://doi.org/10.1007/s00030-022-00825-9
2. M. Gabeleh, R. Plebaniak, Global optimality results for multivalued non-self mappings in b-metric spaces, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas April 2018, Volume 112, Issue 2, pp 347-360
3. R. Plebaniak, Best proximity point theorem in quasi-pseudometric spaces, Abstract and Applied Analysis, Volume 2016 (2016), Article ID 9784592, 1-8.
4. M. Gabeleh, R. Plebaniak, Multivalued SK-contractions with respect to b-generalized pseudodistances. Fixed Point Theory Appl. 2015, 2015:50, 1-20.
5. R. Plebaniak, New generalized fuzzy metrics and fixed point theorem in fuzzy metric space, Fixed Point Theory and Applications, 2014, 2014:241, 1-17.
6. R. Plebaniak, On best proximity points for set-valued contractions of Nadler type with respect to b-generalized pseudodistances in b-metric spaces, Fixed Point Theory and Applications, 2014, 2014:39, 1-13.
7. K. Włodarczyk, R. Plebaniak, New completeness and periodic points of discontinuous contractions of Banach-type in quasi-gauge spaces without Hausdorff property. Fixed Point Theory Appl. 2013, 2013:289, 1-27.
8. K. Włodarczyk, R. Plebaniak, Dynamic processes, fixed points, endpoints, asymmetric structures, and investigations related to Caristi, Nadler, and Banach in uniform spaces. Abstr. Appl. Anal. 2015, Art. ID 942814, 1-16.
9. K. Włodarczyk, R. Plebaniak, Contractions of Banach, Tarafdar, Meir-Keeler, Ćirić-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances, Journal of Mathematical Analysis and Applications 404 (2013), no. 2, 338-350.
10. R. Plebaniak, New generalized pseudodistance and coincidence point theorem in a b-metric space, Fixed Point Theory and Applications, 2013, 2013:270, 1-20.
11. K. Włodarczyk, R. Plebaniak, Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points. Fixed Point Theory Appl. 2013, 2013:128, 1-15.
12. K. Włodarczyk, R. Plebaniak, Leader type contractions, periodic and fixed points and new completivity in quasi-gauge space with generalized quasi-pseudodistances, Topology and Applications 159 (2012), no. 16, 3504-3512.
13. K. Włodarczyk, R. Plebaniak, Generalized uniform spaces, uniformly locally contractive setvalued dynamic systems and fixed points, Fixed Point Theory and Applications, 2012, 2012:104, 1-39.
14. K. Włodarczyk, R. Plebaniak, Contractivity of Leader type and fixed points in uniform spaces with generalized pseudodistances, Journal of Mathematical Analysis and Applications 387 (2012) 533-541.
15. K. Włodarczyk, R. Plebaniak, Robert Fixed points and endpoints of contractive set-valued maps in cone uniform spaces with generalized pseudodistances. Fixed Point Theory Appl. 2012, 2012:176, 1-15.
16. K. Włodarczyk, R. Plebaniak, Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems, Fixed Point Theory and Applications, Volume 2011, Article ID 712706, doi:10.1155/2011/712706, 1-22.
17. K. Włodarczyk, R. Plebaniak, A fixed point theorem of Subrahmanyam type in uniform spaces with generalized pseudodistances, Applied Mathematics Letters 24 (2011) 325-328.
18. K. Włodarczyk, R. Plebaniak, Kannan-type contractions and fixed points in uniform spaces.Fixed Point Theory Appl. 2011, 2011:90, 1-24.
19. K. Włodarczyk, R. Plebaniak, Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudo-distances, Fixed Point Theory and Applications, Volume 2010, Article ID 175453, 35 pages doi:10.1155/2010/175453, 1-37.
20. K. Włodarczyk, R. Plebaniak, Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces. Fixed Point Theory Appl. 2010, Art. ID 864536, 1-32 pp.
21. K. Włodarczyk, R. Plebaniak, C. Obczyński, Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces. Nonlinear Anal. 72 (2010), no. 2, 794–805.
22. K. Włodarczyk, R. Plebaniak, Corrigendum to: "Quasi-asymptotic contractions, set-valued dynamic systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces", Nonlinear Analysis 70 (2009), no. 5, 2143-2144.
23. K. Włodarczyk, R. Plebaniak, Quasi-asymptotic contractions, set-valued dynamic systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces, Nonlinear Analysis 70 (2009), no. 2, 1059-1068.
24. K. Włodarczyk, R. Plebaniak, M. Doliński, Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions. Nonlinear Anal. 71 (2009), no. 10,5022-5031.
25. K. Włodarczyk, R. Plebaniak, A. Banach, Erratum to: "Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces'' [Nonlinear Anal. (2008), doi: 10.1016/j.na.2008.04.037] [MR2503079]. Nonlinear Anal. 71 (2009), no. 7-8, 3585-3586.
26. K. Włodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. Nonlinear Anal. 70 (2009), no. 9, 3332-3341.
27. K. Włodarczyk, R. Plebaniak, Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces, Journal of Mathematical Analysis and Applications 339 (2008), no. 1, 344-358.
28. K. Włodarczyk, R. Plebaniak, Generalized contractions of Meir-Keeler type, endpoints, set-valued dynamical systems and generalized pseudometrics in uniform spaces. Nonlinear Anal. 68 (2008), no. 11, 3445-3453.
29. K. Włodarczyk, R. Plebaniak, C. Obczyński, The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces. Nonlinear Anal. 67 (2007), no. 12, 3373-3383.
30. K. Włodarczyk, R. Plebaniak, C. Obczyński, Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces. Nonlinear Anal. 67 (2007), no. 6, 1668-1679.
31. K. Włodarczyk, D. Klim, R. Plebaniak, Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces. J. Math. Anal. Appl. 328 (2007), no. 1, 46-57.