¹Institute for Systems Science & KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.

¹DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: moaibinu@yahoo.com mathewa@dut.ac.za

² KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
E-mail:  thakur@dut.ac.za

³Institute for Systems Science & Office of the DVC Research, Innovation & Engagement Milena Court,
Durban University of Technology,
 Durban 4000,
South Africa.
E-mail: dvcrie@dut.ac.za

Abstract:

The puzzles in approximating a fixed point of nonlinear problems involving the class of strictly pseudocontractive mappings are conquered in this paper through viscosity implicit rules. Using generalized contraction mappings, a new viscosity iterative algorithm which is implicit in nature is proposed and analysed in Banach spaces for the class of strictly pseudocontractive mappings. The computations and analysis which are used in the proposed scheme are easy to follow and this gives rooms for a broad application of the scheme. It is obtained that the proposed iterative algorithm converges strongly to a fixed point of a μ-strictly pseudocontractive mapping which also solves a variational inequality problem. The result is also shown to hold for finite family of strictly pseudocontractive mappings. A numerical example is given to show the skillfulness of the proposed scheme and its implementation.

Paper's Title:

Applications of the Structure Theorem of (w₁,w₂)-Tempered Ultradistributions

Author(s):

Hamed M. Obiedat and Lloyd E. Moyo

Department of Mathematics,
Hashemite University,
P.O.Box 150459, Zarqa13115,
Jordan.
E-mail: hobiedat@hu.edu.j

Department of Mathematics, Computer Science & Statistics,
Henderson State University,
1100 Henderson Street, Arkadelphia, AR 71999,
USA.
E-mail: moyol@hsu.edu

Abstract:

Using a previously obtained structure theorem for (w₁, w₂)-tempered ultradistributions, we prove that these ultradistributions can be represented as initial values of solutions of the heat equation.

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