Fixed point theorems in uniformly convex Banach spaces

Authors

  • Manoj Karuppasamy Jamal Mohamed College(Autonomous)(Affiliated to Bharathidasan University),Tiruchirapplli-620020, Tamilnadu India.
  • R. Jahir Hussain Jamal Mohamed College(Autonomous)(Affiliated to Bharathidasan University),Tiruchirapplli-620020, Tamilnadu India.

DOI:

https://doi.org/10.23755/rm.v47i0.835

Keywords:

Fixed point, Mann iteration, Ishikawa iteration

Abstract

In this article, we establish a concept of fixed point result in Uniformly convex Banach space. Our main finding uses the Ishikawa iteration technique in uniformly convex Banach space to demonstrate strong convergence. Additionally, we use our primary result to demonstrate some corollaries.

References

V. Berinde. On the convergence of the ishikawa iteration in the class of quasi contractive operators. Acta Math. Univ. Comenianae, LXXIII:1-11, 2004.

L. Bernal-Gonzalez. A schwarz lemma for convex domains in arbitrary banach spaces. Journal of Mathematical Analysis and Applications, 200:511-517, 1996

S. Ishikawa. Fixed points by a new iteration method. Proc. Amer. Math. Soc., 44: 147-150,1974.

H.V. Machado. A chracterization of convex subsets of normed spaces. kodai math-sem.Rep., 25:307-320, 1973.

W. R. Mann. Mean value methods in iteration. Proc. Amer. Math. Soc., 44:506510,1953.

W. A. Takahashi. convexity in metric space and non-expansive mappings. Kodai math.sem rep., 22:142-149, 1970.

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Published

2023-06-30

Issue

Vol. 47 (2023)

Section

Volume 47-2023

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