Some Data Dependence Results From Using $\mathcal{C}$-Class Functions in Partial Metric Spaces

Year 2024, Volume: 7 Issue: 4, 152 - 162

Abdessalem Benterki

https://doi.org/10.32323/ujma.1466879

Abstract

This research paper examines the data dependence of fixed point sets for pseudo-contractive multifunctions in partial metric spaces using the notion of $\mathcal{C}$-class functions. By building upon previous findings from the literature, this work sheds more light on some new perspectives as well as generalizations on this issue. To illustrate how the $\mathcal{C}$-class function can be applied to study the data dependence of fixed point sets for a certain pseudo-contractive multifunction, an illustrative example is given.

Keywords

$\mathcal{C}$-class function, Data dependence, Multifunction, Partial metric space

Ethical Statement

All studies cited in this work adhere to the highest standards of scientific rigour and ethical conduct, and the results are presented in the bibliography.

Supporting Institution

No grants were received from any public, private or non-profit organizations for this research.

References

• [1] A. Benterki, M. Benbachir, Analysis of covid-19 model under Caputo fractional derivative with case study of Algeria, (2023), available at https://doi.org/10.21203/rs.3.rs-3228634/v1
• [2] Y. Mudasir, A. Haroon, L. Chen, H. Maoan, Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations., J. Geom. Phys. 192 (2023), 104955.
• [3] Y. Mudasir, L. Chen, D. Singh (Eds.), Recent Developments in Fixed-Point Theory: Theoretical Foundations and Real-World Applications, Springer Nature Singapore, 2024.
• [4] A. H. Ansari, Note on $\varphi-\psi $-contractive type mappings and related fixed point, Proceedings of the 2nd regional conference on mathematics and applications, PNU (Vol. 377-380) (2014).
• [5] A. H. Ansari, A. Benterki, M. Rouaki, Some local fixed point results under C -class functions with applications to coupled elliptic systems, J. Linear. Topological. Algebra, 7(3) (2018), 169–182.
• [6] T. M. Dosenovic, S. N. Radenovic, Ansari’s method in generalizations of some results in the fixed point theory: Survey, Vojnotehniˇcki Glasnik, 66(2) (2018), 261–280.
• [7] S. G. Matthews, Partial metric topology, Proceedings of the 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728(1) (1994), 183–197.
• [8] E. Karapınar, A fixed point result on the interesting abstract space: Partial metric spaces. Models and Theories in Social Systems, (2019) 375–402.
• [9] I. Beg, A. Akbar, On iteration methods for multivalued mappings, Demonstratio Math., 27(2) (1994), 493-500.
• [10] A. L. Dontchev, W. W. Hager, An inverse mapping theorem for set-valued maps, Proc. Am. Math. Soc., 121 (1994), 481–489.
• [11] J. Saint Raymond, Multivalued contractions, Set-Valued Anal., 2 (1994), 559–571.
• [12] A. Benterki, Some Stability and Data Dependence Results for Pseudo-Contractive Multivalued Mappings, In: Fixed Point Theory and Its Applications to Real World Problems, Nova Science Publisher, New York, (2021), 101–114.
• [13] D. Aze, J. P. Penot, On the dependence of fixed point sets of pseudo-contractive multifunctions: Application to differential inclusions, Nonlinear Dyn. Syst. Theory 6(1) (2006), 31–47.
• [14] T. C. Lim, On fixed point stability for set-valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl., 110 (1985), 436–441.
• [15] J. T. Markin, Continuous dependence of fixed point sets, Proceedings of the American Mathematical Society 38(3)(1973), 545–547.
• [16] I. A. Rus, A. Petrusel, A. Sıntamarian, Data dependence of the fixed points set of multivalued weakly Picard operators, Stud. Univ. Babes-Bolyai, Math. 46(2) (2001), 111–121.
• [17] I. A. Rus, A. Petrusel, A. Sıntamarian, Data dependence of the fixed points set of multivalued weakly Picard operators, Nonlinear Analysis: Theory, Methods & Applications, 52(8) (2003), 1947–1959.
• [18] H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology Appl, 159 (2012), 3234–3242.
• [19] I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778–2785.
• [20] A. Benterki, A local fixed point theorem for set-valued mappings on partial metric spaces, Appl. Gen. Topol., 17(1) (2016), 37–49.
• [21] R. M. Bianchini, M. Grandolfi, Transformazioni di tipo contracttivo generalizzato in uno spazio metrico, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 45 (1968),212–216.
• [22] M. H. Geoffroy, G. Pascaline, Generalized differentiation and fixed points sets behaviors with respect to Fisher convergence, J. Math. Anal. Appl., 387 (2012), 464–474 .
• [23] M. A. Mansour, A. E. Bekkali, J. Lahrache, An extended local principle of fixed points for weakly contractive set-valued mappings, Optimization, 71(5) (2022), 1409–1420.