1. Home
  2. Vol 6, No 1 (2013)
  3. Chidume FAS

An Efficient Algorithm for Zeros of Bounded Generalized Ghi-Quasi-Accretive Maps

C. E. Chidume FAS(1), C. O. Chidume(2), C. O. Chidume(3),


(1) African University of Science and Technology, Abuja.
(2) Auburn University, Auburn, Alabama
(3) Auburn University, Auburn, Alabama
Corresponding Author

Abstract


This is a research announcement of the following result. Let E be a real normed linear space in which the single-valued normalized duality map is Holder continuous on balls and let A: E → E be a bounded generalized Φ-quasi-accretive map. A Mann-type iterative sequence is constructed and proved to converge strongly to the unique zero of A. In particular, our Theorems are applicable in real Banach spaces that include the Lp spaces, 1 < p < ∞. The Theorems are stated here without proofs. The full version of this paper, including detailed technical proofs of the Theorems will be published elsewhere.


Keywords


. Accretive- type operators; Uniformly continuous maps, phi-hemicontractive maps.

References


References

Browder, F. E.; Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 875-882.

[

Browder, F. E.; Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. of Symposia in pure Math. Vol. XVIII, part 2, 1976.

Charles Chidume; Geometric Properties of Banach spaces and Nonlinear Iterations, Springer Verlag Series: Lecture Notes in Mathematics, Vol. 1965, (2009), ISBN 978-1-84882-189-7.

Chidume C. E., Djitte N. and Ezeora J. N.; Convergence theorems for fixed points of uniformly continuous Phi- pseudo- contractive type operator, Accepted, (2013), to appear in: Fixed Point Theory and Applications.

Kato, T.; Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520.

Chang, S.S., Cho, Y.J. and Zhou, H.; Iterative methods for nonlinear operator equations in Banach spaces, Nova Science Publishers, Inc., Huntington, NY (2002).

Gu, F.; Convergence theorems for Φ-pseudo contractive type mappings in normed lnear spaces, Northeast Math. J. 17(2001) no. 3, 340 - 346.

Rockafellar R.T.; Monotone operator and the proximal point algorithm, SIAM J. Control Optim. 14 (1976) 877-898.


Full Text: PDF

Article Metrics

Abstract View : 186 times
PDF Download : 35 times

DOI: 10.57046/TTZB7886

Refbacks

  • There are currently no refbacks.


Copyright (c) 2019 Proceedings of the Nigerian Academy of Science