Fixed points of enriched contraction and almost enriched CRR contraction maps with rational expressions and convergence of fixed points

Abstract

We define enriched Jaggi contraction map, enriched Dass and Gupta contraction map and almost (k, a, b, \lambda)-enriched CRR contraction maps with \lambda=\frac{1}{k+1} in Banach spaces and prove the existence and uniqueness of fixed points of these maps. Further, we show that the sequence of fixed points of the corresponding enriched contraction maps converges to the fixed point of the uniform limit operator of these enriched contraction maps.

Keywords

• enriched Jaggi contraction map
• enriched Dass and Gupta contraction map
• Fixed point.
• Almost (k, a, b, \lambda)-enriched contraction maps

References

1. V. Berinde, Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math. 35(3), (2019), 293-304.
2. V. Berinde, and M. P˘acurar, Fixed point theorems for enriched Ciric-Reich-Rus contractions in Banach spaces and convex metric spaces, Carpathian J. Math., 37(2), (2021), 173-184.
3. B. K. Dass, and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure and Appl. Math., 6 (1975), 1455-1458.
4. D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure and Appl. Math., 8(2), (1977), 223-230.
5. M. Aslantas, H. Sahin and D. Turkoglu, Some Caristi type fixed point theorems, The Journal of Analysis, 29(1), (2021), 89-103.
6. M. Aslantas, H. Sahin and U. Sadullah, Some generalizations for mixed multivalued mappings, Applied General Topology, 23(1), (2022), 169-178.