Approximation fixed points for a system of nonlinear mapping equations

Dissertant

Husayn, Iman Abd al-Wahhab

Thesis advisor

Ahmad, Buthaynah Abd al-Hasan

Comitee Members

Husayn, Mushtaq Sh.
Jamil, Zaynah Z.
Abud, Iman H.
Naji, Raid Kamil

University

University of Baghdad

Faculty

College of Science

Department

Mathematics Department

University Country

Iraq

Degree

Master

Degree Date

2012

English Abstract

Let X be a real Banach space with dual space X∗ , let a mapping J : X → 2 X∗ be the multivalued normalized duality mapping, a mapping T : X → X is said to be α–strongly pseudocontractive mapping if there exists a strictly increasing function α : R + → R + with α(0) = 0 such that for each x, y ∈ X there exists j(x − y) ∈ J(x − y) satisfying: ⟨T x − T y, j(x − y)⟩ ≤ ∥x − y∥ 2 − α(∥x − y∥) ∥x − y∥ .

and a mapping T : X → X is said to be α–strongly hemicontractive mapping if the set of all fixed point,F(T), is nonempty and if there exists a strictly increasing function α : R + → R + with α(0) = 0 such that for each x ∈ X and q ∈ F(T) there exists j(x − q) ∈ J(x − q) satisfying: ⟨T x − q, j(x − q)⟩ ≤ ∥x − q∥ 2 − α(∥x − q∥) ∥x − q∥ , In this thesis we modify and generalize strong convergence theorem for the multi-step iteration sequence to a common fixed point for finite self family of mappings from α–strongly pseudocontractive to α– strongly hemicontractive.

Also we suggest and study a new multi-step iterative algorithms for finding a common fixed point for finite family of self α–strongly hemicontractive mappings.

In the end we study non-self mapping and give a new one-step iteration to compute the fixed point of non-self α–strongly pseudocontractive mapping.

Main Subjects

Mathematics

No. of Pages

79

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-602778