Filomat 2022 Volume 36, Issue 14, Pages: 4947-4961
https://doi.org/10.2298/FIL2214947N
Full text (
230 KB)
Cited by
Solving integral equations via admissible contraction mappings
Nallaselli Gunasekaran (Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram, Chennai, Tamil Nadu, India), gn4255@srmist.edu.in
Gnanaprakasam Arul Joseph (Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram, Chennai, Tamil Nadu, India), aruljoseph.alex@gmail.com
Mani Gunaseelan (Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamil Nadu, India), mathsguna@yahoo.com
Ege Ozgur (Department of Mathematics, Ege University, Bornova, Izmir, Turkey), ozgur.ege@ege.edu.tr
In this article, we introduce a new concept of admissible contraction and
prove fixed point theorems which generalize Banach contraction principle in
a different way more than in the known results from the literature. The
article includes an example which shows the validity of our results, and
additionally we obtain a solution of integral equation by admissible
contraction mapping in the setting of b-metric spaces.
Keywords: Fixed point, b-metric spaces, b-metric-like spaces, α-admissible, applications
Show references
S. Aleksic, Z.D. Mitrovic, S. Radenovic, On some recent fixed point results for single and multivalued mappings in b-metric spaces, Fasc. Math. 61 (2018) 5-16.
M.A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl. 402 (2013) 1-25.
H. H. Alsulami, S. Gulyaz, E. Karapinar, I.M. Erhan, Fixed point theorems for a class of α-admissible contractions and applications to boundary value problem, Abstr. Appl. Anal. 187031 (2014) 1-10.
A.H. Ansari, O. Ege, S. Radenovic, Some fixed point results on complex valued Gb-metric spaces, RACSAM Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. 112(2) (2018) 463-472.
M. Arshad, M. Mudhesh, A. Hussain, E. Ameer, Recent thought of α*-Geraghty F-contraction with application, J. Math. Extension 16(7) (2022) 1-28.
H. Aydi, M.F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 88 (2012) 1-8.
I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30 (1989) 26-37.
M. Bousselsal, On the solvability of some nonlinear functional integral equations on Lp(R+), Filomat 35(6) (2021) 1841-1850.
C. Chen, J. Dong, C. Zhu, Some fixed point theorems in b-metric-like spaces, Fixed Point Theory Appl. 122 (2015).
Lj.B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974) 267-273.
Lj. Ciric, V. Parvaneh, N. Hussain, Fixed point results for weakly α-admissible pairs, Filomat 30(14) (2016) 3697-3713.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 30 (1993) 5-11.
S. Czerwik, Nonlinear set-valued contraction mapping in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena Reeggio Emilia 46 (1998) 263-276.
A.K. Dubey, R. Shukla, R. Dubey, Some fixed point results in b-metric spaces, Asian J. Math. Appl. ama0147 (2014) 1-6.
A. Gholidahneh, S. Sedghi, O. Ege, Z. D. Mitrovic, M. de la Sen, The Meir-Keeler type contractions in extended modular b-metric spaces with an application, AIMS Math. 6(2) (2021) 1781-1799.
I. Hashimoto, H.A. Kudo, Unified concept of admissibility of statistical decision functions, Osaka J. Math. 5 (1968) 137-150.
N. Hussain, E. Karapinar, P. Salimi, F. Akbar, α-admissible mappings and related fixed point theorems, J. Inequal. Appl. 114 (2013) 1-11.
M. Iqbal, A. Batool, O. Ege, M. de la Sen, Fixed point of almost contraction in b-metric spaces, J. Math. 3218134 (2020) 1-6.
M. Iqbal, A. Batool, O. Ege, M. de la Sen, Fixed point of generalized weak contraction in b-metric spaces, J. Funct. Spaces 2042162 (2021) 1-8.
K. Jain, J. Kaur, Some fixed point results in b-metric spaces and b-metric-like spaces with new contractive mappings, Axioms 10 (2021) 55.
E. Karapinar, Fixed points results for α-admissible mapping of integral type on generalized metric spaces, Abstr. Appl. Anal. 141409 (2015) 1-11.
M. Kir, H. Kiziltunc, On some well known fixed point theorems in b-MSs, Turk. J. Anal. Number Theory, 1 (2013) 13-16.
A. Latif, V. Parvaneh, P. Salimi, A.E. Al-Mazrooei, Various Suzuki type theorems in b-metric spaces, J. Nonlinear Sci. Appl. 8 (2015) 363-377.
G. Mani, A.J. Gnanaprakasam, A. Haq, F. Jarad, I.A. Baloch, Solving an integral equation by using fixed point approach in fuzzy bipolar metric spaces, J. Funct. Spaces 9129992 (2021) 1-7.
R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19 (2017) 2153-2163.
S. Mishra, A. K. Dubey, U. Mishra, R.P. Dubey, On some fixed point results for cyclic (α, β)-admissible almost Z-contraction in metric-like space with simulation function, Comm. Math. Appl. 13(1) (2022) 223-233.
N. Mlaiki, N. Dedovic, H. Aydi, M.G. Filipovic, B.B. Mohsin, S. Radenovic, Some new observations on Geraghty and Ciric type results in b-metric spaces, Mathematics 7 (2019) 643.
R. Pant, R. Panicker, Geraghty and Ciric type fixed point theorems in b-metric spaces, J. Nonlinear Sci. Appl. 9 (2016) 5741-5755.
M.A. Ragusa, Parabolic Herz spaces and their applications, Appl. Math. Lett. 25(10) (2012) 1270-1273.
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α − ψ contractive type mappings, Nonlinear Anal. 75 (2012) 2154-2165
M. de la Sen, N. Nicolic, T. Dosenovic, M. Pavlovic, S. Radenovic, Some results on (s − q)-graphic contraction mapping in b-metric-like spaces, Mathematics 7 (2019) 1190.
T.L. Shateri, O. Ege, M. de la Sen, Common fixed point on the bv(s)-metric space of function-valued mappings, AIMS Math. 6(1) (2021) 1065-1074.
S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11(2) (2014) 703-711.
W. Sintunavaat, S. Plubtieng, P. Katchang, Fixed point results and applications on b-metric space endowed with an arbitrary binary relation, Fixed Point Theory Appl. 296 (2013) 1-13.
J. Vujakovic, S. Mitrovic, Z.D. Mitrovic, S. Radenovic, On F-contractions for weak α-admissible mappings in metric-like spaces, Mathematics 8 (2020) 1629.