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

Objective & Hypothesis: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.

📊

Key Findings & Data:It then gives a research result regarding the existence and uniqueness of the fixed point of this innovative type of contractions in Banach spaces.

💡

Conclusion & Impact:Finally, reminds us of the concept of enriched nonexpansive mappings and also offers a simple fixed point theorem for such mappings.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Fixed point · P-contraction · enriched contraction

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

🔖

Cite This Article

Altun, İ., Hançer, H. A., Ateş, M. D. (2024). Enriched P-Contractions on Normed Space and a Fixed Point Result. Turkish Journal of Mathematics and Computer Science, Volume: 16 Issue: 1. https://doi.org/10.47000/tjmcs.1391969

📄 Full Text PDF Viewer

Open in New Tab ↗

↗New Tab

📄

PDF görüntüleyici hazırlanıyor...

References (15)

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).