2. x

3. Examples of Fixed Points Infinite Fixed Points

4. Examples of Fixed Points Unique Fixed Point

5. Examples of Fixed Points There is not a Fixed Point

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

8. Complete Metric space Contraction mapping Mapping has Unique Fixed point

9. 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

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

19. Duality pairing

21. Strictly increasing function Duality pairing

22. Strictly increasing function

23. No

24. Reflexive Banach Space X  X**

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

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

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

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

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

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

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

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

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

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

41. 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

42. 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