x

Examples of Fixed Points Infinite Fixed Points

Examples of Fixed Points Unique Fixed Point

Examples of Fixed Points There is not a Fixed Point

X Metric space T: X  X x y Tx Ty T2xT2x T2yT2y

Complete Metric space Contraction mapping Mapping has Unique Fixed point

The Error: d (x n, p) ≤ (1 − a) −1 a n d (x 1, x 2 ) ; n ∈ N, a ∈ (0,1) x n+1 =Tx n

SpaceMappingIteration Complete Metric space T:X  X Contraction mapping x n+1 =Tx n

Duality pairing

Strictly increasing function Duality pairing

Strictly increasing function

No

Reflexive Banach Space X  X**

SpaceMappingIteration Reflexive Banach Space T:X  X  - strongly pseudocontractive Multi – step

SpaceMappingIteration Reflexive Banach space T i :X  X  - strongly hemicontractive Multi – step

T:C  X C is nonempty convex closed and bounded subset of X

Last result SpacesMappingsIterations Reflexive Banach space T:C  X Nonexpensive One – step

SpaceMappingIteration Reflexive Banach space T:C  X  - strongly pseudocontractive One– step

SpacesMappingsIterations Reflexive Banach Space T i :X  X  - strongly hemicontractive Multi – step

T i :X  X where i=1,2,…N are  - strongly hemicontractive X be reflexive real Banach space Multi-step iterration {x n }

SpaceMappingIteration Reflexive Banach space T:C  X  - strongly pseudocontractive One– step

T : C  X be  - strongly hemicontractive X be reflexive Banach space one-step iterration {x n }

Fixed Point and Iterative Schemes Preliminaries Some Fixed Point Theorem Iterative Schemes

Approximation Fixed Points by Multi-step Iteration Scheme Approximation Fixed Points by Modify Multi-step Iteration Scheme Approximation Fixed Points by Modify Multi-step Iteration Scheme Approximation Fixed Point for a system of Nonlinear α-Strongly Hemicontractive Mapping Equations

Weakly Inward Mapping: Definition and Some Properties Demiclosed Theorem for α-Strongly Pseudocontractive Mapping Approximation Fixed Point for Nonlinear Non-self α-Strongly Pseudocontractive Mapping Approximation Fixed Point for Nonlinear Non-self α-Strongly Pseudocontractive Mapping