Enriched P-Contractions on Normed Space and a Fixed Point Result

Year 2024, , 64 - 69, 30.06.2024

İshak Altun , Hatice Aslan Hançer , Merve Doğan Ateş

https://doi.org/10.47000/tjmcs.1391969

Abstract

This paper introduces the concept of enriched $P$-contractions on linear
normed spaces, and provides illustrative examples that highlight the
differences between this new concept and its previous counterparts. It then
gives a research result regarding the existence and uniqueness of the fixed
point of this innovative type of contractions in Banach spaces. Finally,
reminds us of the concept of enriched nonexpansive mappings and also offers
a simple fixed point theorem for such mappings.

Keywords

Fixed point, P-contraction, enriched contraction, Banach space

References

• Abbas, M., Anjum, R., Ismail, N., Approximation of fixed points of enriched asymptotically nonexpansive mappings in CAT(0) spaces, Rend. Circ. Mat. Palermo, II. Ser, 72(2023), 2409–2427.
• Banach, S., Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fund. Math., 3(1922), 133–181.
• Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35(2019), 293–304.
• Berinde, V., P˘acurar, M., Approximating fixed points of enriched contractions in Banach spaces, J. Fixed Point Theory Appl., 22(2)(2020).
• Berinde, V., P˘acurar, M., Kannan’s fixed point approximation for solving split feasibility and variational inequality problems, J. Comput. Appl. Math., 386(2021).
• Berinde, V., P˘acurar, M., Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative algorithm in Banach spaces, J. Fixed Point Theory Appl., 23(2021), 66.
• Berinde, V., Pa˘curar, M., Fixed point theorems for enriched C´ iric´-Reich-Rus contractions in Banach spaces and convex metric spaces, Carpathian J. Math., 37(2021), 173–184.
• Berinde, V., P˘acurar, M. Fixed points theorems for unsaturated and saturated classes of contractive mappings in Banach spaces, Symmetry, 13(2021), 713.
• Chatterjea, S.K., Fixed-point theorems, C. R. Acad. Bulgare Sci., 25(1972), 727–730.
• Ciric, L.B., A generalization of Banach’s contraction principle, Proc. Am. Math. Soc., 45(1974), 267–273.
• Kannan, R., Some results on fixed points, Bull. Calcutta Math. Soc., 60(1968), 71–76.
• Popescu, O., Fixed point theorem in metric spaces, Bull. of Transilvania Univ., 50(2008), 479–482.
• Reich, S., Some remarks concerning contraction mappings, Canad. Math. Bull., 14(1971), 121–124.
• Rus, I.A., Some fixed point theorems in metric spaces, Rend. Istit. Mat. Univ. Trieste, 3(1971), 169–172.
• Shukla, R., Panicker, R., Approximating fixed points of enriched nonexpansive mappings in geodesic spaces, Journal of Function Spaces, (2022).