References

  1. Acar O., Erdogan E. Some fixed point results for almost contraction on orthogonal metric space. Creat. Math. Inform. 2022, 31 (2), 147–153. doi:10.37193/CMI.2022.02.01
  2. Acar Ö., Erdoğan E., Ozkapu A.S. Generalized integral type mappings on orthogonal metric spaces. Carpathian Math. Publ. 2022, 14 (2), 485–492. doi:10.15330/cmp.14.2.485-492
  3. Alber Y.I., Guerre-Delabriere S. Principle of weakly contractive maps in Hilbert spaces. In: Gohberg I., Lyubich Y. (Eds.) New Results in Operator Theory and Its Applications, 98. Birkhäuser, Basel, 1997.
  4. Babu G.V.R., Lalitha B., Sandhya M.L. Common fixed point theorems involving two generalized altering distance functions in four variables. Proc. Jangjeon Math. Soc. 2007, 10 (1), 83–93.
  5. Boyd D.W., Wong S.W. On nonlinear contractions. Proc. Amer. Math. Soc. 1969, 20 (2), 458–464. doi:10.1090/S0002-9939-1969-0239559-9
  6. Ciric L.B. A generalization of Banach’s principle. Proc. Amer. Math. Soc. 1974, 45, 267–273. doi:10.2307/2040075
  7. Gordji M.E., Habibi H. Fixed point theory in generalized orthogonal metric space. J. Linear Topol. Algebra 2017, 6 (3), 251–260.
  8. Gordji M.E., Rameani M., De La Sen M., Cho Y.J. On orthogonal sets and Banach fixed point theorem. Fixed Point Theory 2017, 18 (2), 569–578. doi:10.24193/fpt-ro.2017.2.45
  9. Gungor N.B. Extensions of orthogonal p-contraction on orthogonal metric spaces. Symmetry 2022, 14 (4), 746. doi:10.3390/sym14040746
  10. Gungor N.B. Some fixed point results via auxiliary functions on orthogonal metric spaces and application to homotopy. AIMS Mathematics 2022, 7 (8), 14861–14874. doi:10.3934/math.2022815
  11. Gungor N.B. Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 2022, 71 (2), 481–489. doi:10.31801/cfsuasmas.970219
  12. Gungor N.B., Turkoglu D. Fixed point theorems on orthogonal metric spaces via altering distance functions. AIP Conf. Proc. 2019, 2183 (1), 040011. doi:10.1063/1.5136131
  13. Hardy G.E., Rogers T.D. A generalization of a fixed point theorem of Reich. Canad. Math. Bull. 1973, 16, 201–206. doi:10.4153/CMB-1973-036-0
  14. Kannan R. Some results on fixed points. Bull. Calcutta Math. Soc. 1968, 10, 71–76.
  15. Khan M.S., Swaleh M., Sessa S. Fixed point theorems by altering distances between the points. Bull. Aust. Math. Soc. 1984, 30 (1), 1–9.
  16. Kübra O. Coupled Fixed Point Results on Orthogonal Metric Spaces with Application to Nonlinear Integral Equations. Hacet. J. Math. Stat. 2023, 52 (3), 619–629. doi:10.15672/hujms.1091097
  17. Naidu S.V.R. Some fixed point theorems in metric spaces by altering distances. Czechoslovak Math. J. 2003, 53 (1), 205–212.
  18. Nallaselli G., Baazeem A.S., Gnanaprakasam A.J., Mani G., Javed K., Ameer E., Mlaiki N. Fixed Point Theorems via Orthogonal Convex Contraction in Orthogonal \(\flat\)-Metric Spaces and Applications. Axioms 2023, 12 (2), 143. doi:10.3390/axioms12020143
  19. Özlem A., Özkapu A.S. Multivalued rational type F-contraction on orthogonal metric space. AIMS Math. Found. Comp. 2023, 6 (3), 303–312. doi:10.3934/mfc.2022026
  20. Reich S. Kannan’s fixed point theorem. Boll. Unione Mat. Ital. 1971, 4 (4), 1–11.
  21. Rhoades B.E. Some theorems on weakly contractive maps. Nonlinear Anal. 2001, 47 (4), 2683–2693. doi:10.1016/S0362-546X(01)00388-1
  22. Sastry K.P.R., Babu G.V.R. Some fixed point theorems by altering distances between the points. Indian J. Pure Appl. Math. 1999, 30 (6), 641–647.
  23. Sastry K.P.R., Naidu S.V.R., Babu G.V.R., Naidu G.A. Generalization of common fixed point theorems for weakly commuting maps by altering distances. Tamkang J. Math. 2000, 31 (3), 243–250. doi:10.5556/j.tkjm.31.2000.399
  24. Sawangsup K., Sintunavarat W. Fixed point results for orthogonal Z-contraction mappings in O-complete metric space. Int. J. Appl. Phys. Math 2020, 10 (1), 33–40. doi:10.17706/ijapm.2020.10.1.33-40
  25. Senapati T., Dey L.K., Damjanovic B., Chanda A. New fixed point results in orthogonal metric spaces with an application. Kragujevac J. Math. 2018, 42 (4), 505–516. doi:10.5937/KGJMATH1804505S
  26. Shaeri M.R., Asl J.H., Gordji M.E., Refaghat H. Common fixed point (\(\alpha_*\)-\(\psi\)-\(\beta_i\))-contractive set-valued mappings on orthogonal Branciari \(S_ {b}\)-metric space. Int. J. Nonlinear Anal. Appl. 2023, 14 (12), 105–120. doi:10.22075/ijnaa.2023.27426.3597