Common fixed-point for a pair of Hardy-Rogers F-contractions in Quasi partial b-Metric space
Résumé
This paper aims to prove common fixed point theorems for a pair of Hardy-Rogers F-contractions in the setting of quasi-partial b- metric space. The main theorem generalizes the results due to Wardowski and many others in the literature. We also provide an illustrative example and an application to boundary value problem to validate the results.
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Références
A. Gupta, and P. Gautam, Quasi-partial b- metric space and some related fixed point theorems, Fixed point Theory Appl, ( 18),56-61, (2015). https//doi.org/10.1186/s13663-015-0260-21.
A. Taheri and A. P. Farajzadeh, A new generalization of α-type almost-F-contractions and α-type F-Suzuki contractions in metric spaces and their fixed point theorems, Carpathian Mathematical Publications, 11(2), 475-492, (2019).
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications, 94, (2012).
D. Wardowski, Solving existence problems via F-contractions, Proceedings of the AMS, vol., 146,1585–1598, (2018).
D. Wardowski and N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstratio Mathematica, 47(1), 146-155, (2014).
F. E. Browder, on convergence of successive approximations for nonlinear functional equations, Nederl. Akad.Wetensch. Proc.Ser, 30,27-35, (1968).
G. Minak, A. Helvaci and I. Altun, ´ Ciri´c type generalized F-contractions on complete metric spaces and fixed point results, Filomat, 28(6), 1143-1151, (2014).
H. Kunzi, P. Homeira, and P. Michel Schellekens, Partial quasi-metrics, Theoretical Computer Science, 365(3), 237-246, (2006).
H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory and Applications, 210, (2014).
I. A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal., 30, 26-37, (1989).
L. Scholastica, S. Kumar and G. Kakiko Fixed Points for F-contraction Mappings in Partial Metric Spaces, Lobachevskii Journal of Mathematics, 40(2), 183:188, (2019).
L. Wangwe, and S. Kumar, Fixed Points Results for Interpolative ϕ-Hardy-Rogers type Contraction Mappings in Quasi-Partial b-Metric Space with some Applications, Journal of Analysis, 18 pages, (2022).
L. Wangwe, S. Kumar, Common Fixed Theorems for Generalized F-Kannan mapping in Metric Space with an Applications, Abstact and Applied Analysis, Vol.2021, Article ID 6619877,12 pages,(2021).
M. Abbas, B. Ali, and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory and Applications, (1), 1-11, (2013).
M. Arshad, S. U. Khan, and J. Ahmad, Fixed point results for F-contractions involving some new rational expressions, JP Journal of Fixed Point Theory and Applications, 1, (2016).
N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed PointTheory Appl, Article ID 277 .doi:10.1186/1687-1812-2013-277.
N. Hussain, V. Parvaneh, J. R. Roshan, and Z. Kadelburg, Fixed points of cyclic (y, j, L, A, B)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory and Applications, Article No 256, (2013).
P. Kumam, N. V. Dung, and K. Sitthithakerngkiet, A generalization of ´ Ciri´c fixed point theorem, Filomat, vol. 29, no. 7,1549–1556, (2015).
P. Gautam, S. Kumar, S. Verma, and S. Gailati, On some ω-Interpolative Contractions of Suzuki-type Mappings in Quasi-Partial b-Metric space, Journal of Function Spaces, Vol. 2022, Article id.9158199, 12pages, (2022).
S. Banach, Sur les operationes dans les ensembles abstraits et leur application aux equation integrales, Fund. Math, ( 3), 133-181, (1922).
S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math, 30 , no. 2, 475–488, (1969).
S. S. Chang, J. Kim, L. Wang and J. Tang, Existence of fixed points for generalized F-contractions and generalized F-suzuki contractions in metric spaces, Global Journal of Pure and Applied Mathematics, 12(6), 4867-4882, (2016).
S. G. Metthews, partial metric topology, Ann.N.Y. Acad.Sci, 728, 183–197, (1994).
S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulg. Sci, 25, 727–730, (1972).
S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterranean Journal of Mathematics, (2013), https//doi.org/10.1007/s00009-013-0327-4.
S. Kumar, Coincidence Points for a pair of Ordered F-contraction Mappings in Ordered Partial Metric Spaces, Malaya Journal of Mathematics, 7(3), 423-428, (2019).
S. Kumar, and M. Asim, Fixed Point Theorems for a pair of F-contraction mappings in Ordered Metric Space, Advances in Nonlinear Variational Inqualities, Vol.25, 17:28, (2022).
S. Pauline and S.Kumar, Common Fixed Point theorems for T-Hardy-Rogers contraction Mappings in Complete Coneb-Metric Spaces with an application, Topol. Algebra Appl., ,9:105-117, (2021).
T. C. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861-1869, (2008).
T. Suzuki, Several fixed point theorems in complete metric spaces, Yokohama Math. Journal Vol. 44, (1997).
W. Sintunavarat, S. Plubtieng and P. Katchang, Fixed point result and applications on b-metric space endowed with an arbitrary binary relation, Fixed Point Theory and Applications, Article No 296, (2013).
Z. Mustafa, J. R. Roshan, V. Parvaneh and Z. Kadelburg, Some common fixed point result in ordered partial b-metric spaces, Journal of Inequalities and Applications, 2013:562, (2013).
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