Exploring Fixed Point Results in Perturbed Controlled Metric Space

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-231
Published: Aug 3, 2026
Cite as:
Rajagopalan Ramaswamy, Neha Bhardwaj, Manoj Kumar, Gunaseelan Mani, Abdulkareem Saleh Hamarsheh, S. Padmaja, Exploring Fixed Point Results in Perturbed Controlled Metric Space, Int. J. Anal. Appl., 24 (2026), 231.

Main Article Content

Rajagopalan Ramaswamy, Neha Bhardwaj, Manoj Kumar, Gunaseelan Mani, Abdulkareem Saleh Hamarsheh, S. Padmaja

Abstract

In this manuscript, we shall introduce the notion of perturbed controlled metric spaces, where the control function is modified by an additional perturbation term. We establish fixed point theorems in this framework, demonstrating how classical results can be extended to perturbed settings. To prove the validity of our results some suitable examples are also provided. Some results from the literature are also deduced from our main theorems. Non trivial example and an application to solve integral equation have been provided to support the derived result.

Article Details

References

  1. S. Banach, Sur les Opérations dans les Ensembles Abstraits et Leur Application aux Equations Intégrales, Fundam. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181.
  2. D.W. Boyd, J.S.W. Wong, On Nonlinear Contractions, Proc. Amer. Math. Soc. 20 (1969), 458-458. https://doi.org/10.1090/s0002-9939-1969-0239559-9.
  3. S. Reich, Fixed Points of Contractive Functions, Boll. Unione Mat. Ital. 5 (1972), 26-42.
  4. L.B. Ciric, A Generalization of Banach's Contraction Principle, Proc. Amer. Math. Soc. 45 (1974), 267-273. https://doi.org/10.2307/2040075.
  5. S. Czerwik, Contraction Mappings in b-Metric Spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
  6. A. Branciari, A Fixed Point Theorem of Banach-Caccioppoli Type on a Class of Generalized Metric Spaces, Publ. Math. Debr. 57 (2000), 31-37. https://doi.org/10.5486/pmd.2000.2133.
  7. N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled Metric Type Spaces and the Related Contraction Principle, Mathematics 6 (2018), 194. https://doi.org/10.3390/math6100194.
  8. O. Popescu, Some Remarks on the Paper “Fixed Point Theorems for Generalized Contractive Mappings in Metric Spaces”, J. Fixed Point Theory Appl. 23 (2021), 72. https://doi.org/10.1007/s11784-021-00908-7.
  9. H. Huang, X. Fu, Asymptotic Properties of Solutions for Impulsive Neutral Stochastic Functional Integro-Differential Equations, J. Math. Phys. 62 (2021), 013301. https://doi.org/10.1063/1.5139964.
  10. G. Mani, R. Ramaswamy, A.J. Gnanaprakasam, A. Elsonbaty, O.A. Abdelnaby, et al., Application of Fixed Points in Bipolar Controlled Metric Space to Solve Fractional Differential Equation, Fractal Fract. 7 (2023), 242. https://doi.org/10.3390/fractalfract7030242.
  11. R. Ramaswamy, G. Mani, A.J. Gnanaprakasam, O.A. Abdelnaby, S. Radenović, Solving an Integral Equation via Tricomplex-Valued Controlled Metric Spaces, Axioms 12 (2023), 56. https://doi.org/10.3390/axioms12010056.
  12. R. Ramadan, O. Ege, R. Ramaswamy, Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations, Fractal Fract. 9 (2025), 527. https://doi.org/10.3390/fractalfract9080527.
  13. M. Kumar, N. Bhardwaj, G. Mani, R. Ramaswamy, K. Hayat Khan, et al., Fixed Point Theorems for (β, φ)-Expansive Mappings in Controlled Metric Space, Eur. J. Pure Appl. Math. 18 (2025), 7124. https://doi.org/10.29020/nybg.ejpam.v18i4.7124.
  14. M. Penumarthy Parvateesam, C.P. Dhuri, R. Ramaswamy, K.H. Khan, O.A. Abdelnaby, Common Fixed Point Theorems for Mappings Satisfying Implicit Relation in Bipolar Metric Space, Eur. J. Pure Appl. Math. 18 (2025), 5982. https://doi.org/10.29020/nybg.ejpam.v18i2.5982.
  15. M. Jleli, B. Samet, On Banach's Fixed Point Theorem in Perturbed Metric Spaces, J. Appl. Anal. Comput. 15 (2025), 993-1001. https://doi.org/10.11948/20240242.
  16. C. Li, J. Llibre, Uniqueness of Limit Cycles for Liénard Differential Equations of Degree Four, J. Differ. Equ. 252 (2012), 3142-3162. https://doi.org/10.1016/j.jde.2011.11.002.
  17. F. Vetro, Fixed Point for α-Θ-Φ-Contractions and First-Order Periodic Differential Problem, RACSAM. Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 113 (2018), 1823-1837. https://doi.org/10.1007/s13398-018-0586-9.