## Table of Contents

** 1. Local Convergence for a Two-Step Third Order Secant-Like Method Without Bilinear Operators**

1. Introduction

2. Convergence

References

**2. Semi-Local Convergence for a Derivative Free Method with Error Controlled Iterates for Solving Nonlinear Equations**

1. Introduction

2. Convergence of Majorizing Sequences

3. Convergence of Method (2.2)

References

**3. On the Semi-Local Convergence of a Sharma-Gupta Fifth Order Method for Solving Nonlinear Equations**

1. Introduction

2. Convergence

References

**4. On the Semi-Local Convergence of a Seventh Order Method for Nonlinear Equations Convergence for a Seventh Order Method for Equations**

1. Introduction

2. Semi-Local Convergence

References

**5. On the Semi-Local Convergence of a Fifth Order Method for Solving Nonlinear Equations**

1. Introduction

2. Sequences Majorizing Method (5.2)

3. Analysis for Method (5.2)

References

**6. On the Semi-Local Convergence of a Fifth Order Efficient Method for Solving Nonlinear Equations**

1. Introduction

2. Semi-Local Analysis

References

**7. Improved Convergence of Derivative-Free Halleyâ€™s Scheme with Two Parameters**

1. Introduction

2. Semi-Local Convergence I

3. Semi-Local Convergence Part 2

References

**8. Extended Convergence for a Third Order Traub-Like Method with Parameter for Solving Equations**

1. Introduction

2. Majorizing Sequence

3. Convergence of Method (8.3)

4. Numerical Experiments

References

**9. Ball Convergence Comparison for Methods Whose First Step is Given by Newtonâ€™s for Solving Nonlinear Equations**

1. Introduction

2. Ball Convergence

References

**10. Extending The Convergence of a Steffensen-Like Method Without Derivatives for Solving Nonlinear Equations**

1. Introduction

2. Majorizing Sequences

References

**11. On the Semi-Local Convergence of a Fourth Order Derivative Free Two-Step Steffensen Method for Solving Equations**

1. Introduction

2. Majorizing Sequences

3. Convergence for Method (11.2)

References

**12. A Semi-Local Convergence for a Class of Fourth Order Method for Solving Equations**

1. Introduction

2. Semi-Local Convergence

References

**13. Local Convergence Comparison Between Two Competing Fifth Order Iterations**

1. Introduction

2. Real Majorizing Function

3. Local Analysis

References

**14. Semi-Local Convergence Analysis of High Convergence Order Iterations Under the Same Set of Conditions**

1. Introduction

2. Semi-Local Analysis

3. Numerical Example

References

**15. A Collection of Iterative Methods with Order Five, Six and Seven and Their Semi-Local Convergence**

1. Introduction

2. Convergence Criteria

References

**16. Extended Semi-Local Convergence Analysis for the Two-Step Newton Method Under Generalized Lipschitz Conditions**

1. Introduction

2. Semi-Local Convergence

References

**17. Semi-Local Convergence for Jarratt-Like Methods Under Generalized Conditions for Solving Equations**

1. Introduction

2. SL of Method (17.3) and Method (17.2)

References

**18. On The Semi-Local Convergence of a Derivative Free Fourth Order Method for Solving Equations**

1. Introduction

2. Majorizing Sequence

3. Semi-Local Convergence

References

**19. Extended and Unified Kantorovich Theory for Solving Generalized Nonlinear Equations**

1. Introduction

2. Mathematical Background

3. Majorizing Sequence

4. Main Result

References

**20. A Derivative Free Two-Step Fourth Order Method for Solving Equations in Banach Space**

1. Introduction

2. Local Convergence Analysis

References

**21. Local Convergence for An Efficient Derivative Free Fourth Order Method for Solving Equations in Banach Space**

1. Introduction

2. Convergence

References

**22. Extended Local Convergence of Steffensen-Type Methods for Solving Nonlinear Equations in Banach Space**

1. Introduction

2. Local Analysis of STM

References

**23. Extended Convergence Analysis of Optimal Eighth Order Methods for Solving Nonlinear Equations in Banach Space**

1. Introduction

2. Local Convergence

3. Special Cases

References

**24. Efficient Fifth Convergence Order Methods for Solving Equations in Banach Space**

1. Introduction

2. Local Convergence

3. Semi-Local Convergence

References

**25. Efficient Derivative Free Seventh Order Methods for Solving Equations in Banach Space**

1. Introduction

2. Convergence for method (25.4)

3. Special Cases

4. Convergence of method (25.7)

References

**26. Necessary and Sufficient Conditions for the Q-Order of Convergence of Iterative Methods**

1. Introduction

2. Local Convergence

References

**27. Necessary and Sufficient Conditions for the Convergence of Sixth Order or Higher Derivative Free Methods**

1. Introduction

2. Local Convergence

References

**28. The Convergence Analysis of Some Fourth and Fifth Order Methods**

1. Introduction

2. Local Convergence

3. Semi-Local Convergence

References

**29. High Convergence Order Derivative Free Methods-I**

1. Introduction

2. Local Convergence Analysis

3. Semi-Local Convergence

References

**30. High Convergence Order Derivative Free Methods-II**

1. Introduction

2. Local Convergence

3. Semi-local Convergence

References

**31. High Convergence Order Derivative Free Methods -III**

1. Introduction

2. Local Convergence

3. Semi-Local Convergence

References

**32. Fourth Convergence Order Derivative Free Methods with or Without Memory**

1. Introduction

2. Local Convergence

3. Semi-Local Convergence

References

**33. Convergence Radius of an Efficient Iterative Method with Frozen Derivatives**

1. Introduction

2. Convergence for method (33.2)

3. Numerical Examples

References

**34. A Comparison Between Some Derivative Free Methods**

1. Introduction

2. Local Convergence

References

**35. High Convergence Order Methods**

1. Introduction

2. Semi-Local Convergence

References

**36. On a Family of Optimal Eighth Order Methods for Equations in Banach Space**

1. Introduction

2. Local Analysis

References

**37. Extended Ball Convergence of a Xiao-Yin Fifth Order Scheme for Equations**

1. Introduction

2. Ball convergence

3. Numerical Experiments

References

**38. On the Semi-Local Convergence of Kingâ€™s Fourth Order Method for Solving Equations**

1. Introduction

2. Scalar Majorizing Sequences

3. Analysis

4. Convergence Result for Method 38.3

5. Applications

References

**39. On the Convergence of two Eighth Order Methods with Divided Differences and Derivatives**

1. Introduction

2. Local Convergence

3. Semi-Local Convergence

References

**40. Bilinear Operator Free Method for Solving Nonlinear Equations**

1. Introduction

2. History of the Procedure

3. Convergence Analysis

4. Numerical Experiments

References