Dr. Malik Muhammad Arif Rafique
  • List of Publications (Indexed/Referred/ Reviewed)

    1. A. Rafiq, Generalized vector products and their applications in Pure and Applied Mathematics, American Mathematical Society, Abstracts No. 98T-15-92, 19 (3) PP 488 (1998).

    2. J. U. Jeong, M. A. Noor, A. Rafiq, Noor iterations for nonlinear Lipschitzian strongly accretive mappings, Journal of Korean Math. Series B: Pure Appl. Math. 11 (4) (2004), 339-350.

    3. A. Rafiq, N. A. Mir, An Ostrowski type inequality for p-norms, Journal of Mathematical Inequalities in Pure and Applied Mathematics, Volume 7, Issue 3, Article 112, 2006.

    4. A. Rafiq, A note on the theorem of V. Berinde, DEMONSTRATIO MATHEMATICA XXXIX 4 (2006), 863-867.

    5. A. Rafiq, Modified Noor iterations for nonlinear equations in Banach Spaces, Appl. Math. Comput. 182 (1) ( 2006), 589-595.

    6. A. Rafiq, On Mann iteration in Hilbert spaces, Nonlinear Analysis 66 (2007), 2230–2236.

    7. A. Rafiq, A convergence theorem for Mann fixed point iteration procedure, Applied Mathematics Electronic Notes 6 (2006), 294-303.

    8. A. Rafiq, Strong convergence of a modified implicit iteration process for a finite family of Z-operators, International Journal of Mathematics and Mathematical Sciences Volume 2006 (2006), Article ID 10328, 6 pages.

    9. A. Rafiq, On the convergence of the modified Noor iteration process with errors in the class of quasi-contractive operators, Journal of the Korea Society of Mathematical Education Series B: Pure and Applied Mathematics 13 (1) (2006), 39-46.

    10. A. Rafiq, Strong convergence of an implicit iteration process for a finite family of quasi-contractive operators, DEMONSTRATIO MATHEMATICA XL 1 (2007), 203-208.

    11. N. A. Mir, A. Rafiq, A Note on Ostrowski Like Inequalities in L1(a,b) Spaces, General Mathematics 14 (1) (2006), 23-30.

    12. A. Rafiq, On the convergence of the three-step iteration process in the class of quasi-contractive operators, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 22 (2006), 1-5.

    13. A. Rafiq, N. A. Mir, Fiza Zafar, A generalized Ostrowski-Grüss type inequality for twice differentiable mappings and applications, Journal of Mathematical Inequalities in Pure and Applied Mathematics, Volume 7, Issue 4, Article 124, 2006.

    14. A. Rafiq, N. S. Barnett, Weighted Ostrowski’s type inequality for cumulative distribution functions, Journal of Mathematical Inequalities in Pure and Applied Mathematics, Volume 7, Issue 5, Article 188, 2006.

    15. A. Rafiq, Convergence of an iterative scheme due to Agarwal et al., Rostock. Math. Kolloq. 61 (2006), 95–105.

    16. A. Rafiq, Strong convergence of an implicit iteration process with errors for a finite family of ψ-uniformly pseudocontractive and ψ-uniformly accretive mappings in Banach spaces, Nonlinear functional analysis and applications 11 (4) (2006), 589-596.

    17. A. Rafiq, Fixed points of quasi-contractive operators in normed spaces, Mathematical Communications 11 (2006), 115-120.

    18. A. Rafiq, Implicit fixed point iterations, Rostock. Math. Kolloq. 62 (2007), 21-39.

    19. A. Rafiq, On the convergence of implicit Noor iterations in convex metric spaces, Nonlinear Analysis Forum 11 (1) (2006), 53-60.

    20. A. Rafiq, Common fixed points through implicit iteration process with errors, Fixed Point Theory 8 (1) (2007), 105-113.

    21. A. Rafiq, On the equivalence of Mann and Ishikawa iteration methods with errors, Mathematical Communications 11 (2006), 141-150.

    22. A. Rafiq, Sundus Zafar, On the convergence of Implicit Ishikawa iterations with errors to a common fixed point of two mappings in convex metric spaces, General Mathematics 14 (2) (2006), 95-108.

    23. F. Ahmad, A. Rafiq, N. A. Mir, Weighted Ostrowski type inequality for twice differentiable mappings, Global Journal of Research in Pure and applied Mathematics 2 (2) (2006), 147-154.

    24. A. Rafiq, F. Ahmad, N. A. Mir, New Ostrowski-Gruss type inequalities, International Journal of Applied Mathematics 20 (4) (2007), 483-493.

    25. A. Rafiq, Some convergence theorems for asymptotically pseudocontractive mappings, Kodai Math. Journal 30 (2006), 74–84.

    26. A. Rafiq, F. Ahmad, Another weighted Ostrowski-Gruss type inequality for twice differentiable mappings, Krajujevac Journal of Mathematics 31 (2008), 43-51.

    27. A. Rafiq, Fixed points of Ciric quasi-contractive operators in generalized convex metric spaces, General Mathematics 14 (4) (2006), 79-80.

    28. A. Rafiq, S. Hussain, F. Ahmed, M. Awais, Fiza Zafar, An efficient three-step iterative method with sixth order of convergence for solving nonlinear equations, International Journal of Computer Mathematics 84 (3) (2007), 369-375.

    29. A. Rafiq, S. Hussain, F. Ahmed, M. Awais, New iterative methods, Appl. Math. Compt. 189 (2) (2007), 1260-1267.

    30. N. A. Mir, A. Rafiq, F. Ahmed, Generalization of integral inequalities for functions whose modulus of nth derivatives are convex, General Mathematics 14 (4) (2006), 67-92.

    31. A. Rafiq, Strong convergence of an implicit iteration process with errors for a finite family of nonexpansive mappings, Nonlinear Analysis Forum 11 (2) (2006), 165-174.

    32. A. Rafiq, M. Awais, Fiza Zafar, Modified efficient variant of super-Halley method, Appl. Math. Compt. 189 ( 2) (2007), 2004-2010.

    33. F. Ahmed, A. Rafiq, S. Hussain, N. A. Mir, New iterative method with sixth order of convergence, International Journal of Computational and Numerical Analysis and Applications 6 (4) (2004), 391-399.

    34. A. Rafiq, F. Ahmed, Ostrowski Grüss Cebysev type inequalities for functions whose second derivatives belong to L1(a,b) spaces and whose modulus of second derivatives are convex, Revista Colombiana de Matemáticas 41 (1) (2007), 1-13.

    35. A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Compt. 195 (2) (2008), 819-821.

    36. A. Rafiq, A note on ”New family of iterative methods for nonlinear equations, Appl. Math. Compt. 192 (1) ( 2007), 280-282.

    37. A. Rafiq, Mann iterative scheme for nonlinear equations, Mathematical Communications 12 (2007), 25-31.

    38. A. Rafiq, N. A. Mir, F. Ahmed, Weighed Cebysev-Ostrowski type inequalities involving functions whose first derivatives belong to L∞(a,b), Applied Mathematics and Mechanics 28 (7) (2007), 901-906.

    39. F. Ahmed, A. Rafiq, N. A. Mir, Open quadrature iterative scheme, International Journal of Applied Mathematics 20 (6) (2007), 787-799.

    40. A. Rafiq, A note on “New classes of iterative methods for nonlinear equations” and “Some iterative methods free from second derivatives for nonlinear equations”, Appl. Math. Compt. 193 (2) (2007), 572-576.

    41. A. Rafiq, N. A. Mir, S. Hussain, Some inequalities of Aczel type for Gramians in n-inner product spaces, DEMONSTRATIO MATHEMATICA 40 (3) (2007), 609-629.

    42. Lj. B. ´Ciri´c, A. Rafiq, Strong convergence theorems for asymptotically nonexpansive mappings, International Journal of Applied Mathematics and Mechanics 4 (1) (2008), 1-11.

    43. N. A. Mir, A. Rafiq, F. Ahmed, Weighted Ostrowski type inequality for differentiable mappings whose first derivatives belong to L∞(a,b), General Mathematics 14 (3) (2006), 24-35.

    44. A. Rafiq, N. A. Mir, F. Ahmed, Weighted Ostrowski type inequality for differentiable mappings whose first derivatives belong to Lp (a,b), General Mathematics 14 (3) (2006), 91-102.

    45. A. Rafiq, F. Ahmad, S. Hussain , Some new sixth order variants of Newton's method, Nonlinear Analysis Forum 12 (1) (2007), 85-90.

    46. A. Rafiq, Ishikawa iteration scheme for asymptotically nonexpansive mappings on uniformly convex metric spaces, Nonlinear Analysis Forum 12 (1) (2007), 17-27.

    47. Lj. B. Ćirić, A. Rafiq, S. Radenović, M. Rajović, J. S. Ume, On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings, Appl. Math. Compt. 198 (1) (2008), 128-137.

    48. A. Rafiq, Common fixed points of quasi-contractive operators, General Mathematics 16 (2) (2008), 49-58.

    49. A. Rafiq, Fiza Zafar, N. A. Mir, A generalization of Ostrowski-Grüss type inequality for twice differentiable mappings in Euclidean norm, General Mathematics 16 (3) (2008), 51-72.

    50. A. Rafiq, On iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings, Nonlinear Analysis Forum 12 (2) (2007), 179–182.

    51. A. Rafiq, Iterative solution of nonlinear equations involving generalized Φ-hemicontractive mappings, Indian Journal of Mathematics 50 (2) (2008), 1-22.

    52. A. Rafiq, Fiza Zafar, New bounds for the first inequality of Ostrowski-Grüss type and applications in numerical integration, Nonlinear Functional Analysis and Applications 12 (1) (2007), 75-85.

    53. A. Rafiq, On steepest descent approximations, Nonlinear Functional Analysis and Applications 13 (4) (2008), 665-672.

    54. A. Rafiq, Uniformly L-Lipschitzian Mappings, Bulletin of AMS 23 (1) (2008), 1-13.

    55. A. Rafiq, A. M. Acu, M. Acu, Steepest descent approximations in Banach space, General Mathematics 16 (3) (2008), 133-143.

    56. A. Rafiq, A. M. Acu, Strong convergence of an implicit iteration process with errors for a finite family of strongly pseudocontractive mappings, Annals of Oradea University- Mathematica fascicola XVI (2009), 133–139.

    57. A. M. Acu, M. Acu, A. Rafiq, The estimate for the remainder term of some quadrature formulae, ACTA UNIVERSITATIS APULENSIS 16 (2008), 53-62.

    58. N. A. Mir, A. Rafiq, M. Rizwan, Ostrowski Grüss Čebyšev type inequalities for functions whose modulus of second derivatives are convex, General Mathematics 16 (3) (2008), 73-97.

    59. B. S. Lee, A. Rafiq, An Iterative algorithm for asymptotically pseudocontractive mappings, Nonlinear Analysis Forum 13 (1) (2008), 49-56.

    60. A. Rafiq, B. S. Lee, Mann iterative process with error term for pseudocontractive mappings, Nonlinear Analysis Forum 13 (1) (2008), 77-83.

    61. F. Ahmed, A. Rafiq, Fifth-order iterative scheme using decomposition technique, Nonlinear Analysis Forum 13 (1) (2008), 95-102.

    62. N. A. Mir, K. Ayub, A. Rafiq, A third order convergent iterative method for solving non-linear equations, International Journal of Computer Mathematics, First Published on: 10 October 2008, DOI: 10.1080/00207160802218704.

    63. A. Rafiq, A. M. Acu, On fixed points of pseudocontractive mappings, ACTA UNIVERSITATIS APULENSIS 16 (2008), 63-69.

    64. Lj. B. Ćirić, A. Rafiq , N. Cakić, J. S. Ume, Implicit Mann fixed point iterations for pseudocontractive mappings, Applied Mathematics Letters 22 (4) (2009), 581-584.

    65. A. Rafiq, M. Ahmad, S. Hussain, A General Approach to Specific Second Order Ordinary Differential Equations using Homotopy Perturbation Method, Physics Letters A 372 (30) (2008), 4973-4976.

    66. A. M. Acu, M. Acu, A. Rafiq, Extremal problems with polynomials, General Mathematics 16 (4) (2008), 3-14.

    67. A. Rafiq, N. A. Mir, Fiza Zafar, A generalized Ostrowski type inequality for a random variable whose probability density function belongs to L1[], DEMONSTRATIO MATHEMATICA XLI 3 (2008), 723-732.

    68. A. Rafiq, Implicit fixed point iterations for pseudocontractive mappings, KODAI MATH. J. 32 (1) (2009), 146-158.

    69. Lj. B. C´iric´, A. Rafiq, N. Cakic´, J. S. Ume, On fixed points of two asymptotically quasi nonexpansive mappings, International Journal of Applied Mathematics and Mechanics (2010), in press.

    70. A. Rafiq, A. M. Acu, Common fixed points of Ciric quasi-contractive operators through Ishikawa iteration process with errors, General Mathematics 16 (3) (2008), 145–157.

    71. A. Rafiq, N. A. Mir, Fiza Zafar, A generalized Ostrowski type inequality for a random variable whose probability density functions belongs to Lp[a,b], Appl. Math. E-Not s 8 (2008), 246-253.

    72. M. Y. Malik, A. Rafiq, Two-dimensional fin with convective base condition, Nonlinear Analysis: Real World Applications 11 (1) (2010), 147-154.

    73. Lj. B. Ćirić, A. Rafiq, N. Cakić, On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings, Nonlinear Analysis: Theory, Methods & Applications 70 (12) (2009), 4332-4337.

    74. R. A. Rashwan, A. Rafiq, A. A. A. Hakim, On the convergence of three-step iteration process with errors in the class of quasi-contractive operators, Proc. Pakistan Acad. Sci. 46 (1) (2009), 41-46.

    75. A. Rafiq, F.Ahmad, On weighted Ostrowski type inequalities in L1(a, b) spaces, Mathematical Communications 14 (1) (2009), 27-33.

    76. A. Rafiq, M. Awais, Convergence on the homotopy continuation method 4 (6) (2008), 62 – 70.

    77. A. Rafiq, S. Hussain, M. Ahmed, General homotopy method for Lane-emden type differential equations, International Journal of Applied Mathematics and Mechanics 5 (3) (2009), 75-83.

    78. A. Rafiq, M. Rafiullah, Some new multi-step iterative methods for solving nonlinear equations using modified homotopy perturbation method, Nonlinear Analysis Forum 13 (2) (2008), 185–194.

    79. B. S. Lee, A. Rafiq, Composite implicit iterative process for family of strictly pseudocontractive mappings, Nonlinear Analysis Forum 13 (2) (2008), 195–204.

    80. A. Rafiq, A note on “approximating fixed points of holomorphic mappings in the hilbert ball”, Nonlinear Analysis Forum 13 (2) (2008), 215–216.

    81. A. Rafiq, A. M. Acu, M. Acu, Iterations of asymptotically pseudocontractive mappings in Banach spaces, General Mathematics 17 (1) (2009), 113–124.

    82. A. Rafiq, A. Javeria, New iterative methods for solving nonlinear equations by using modified homotopy perturbation method, ACTA UNIVERSITATIS APULENSIS 18/2009, 129-137.

    83. A. Rafiq, B. S. Lee, D. Djoric, Some results on three asymptotically pseudocontractive mappings, Journal of Advanced Research in Applied Mathematics 1 (2) (2009), 19-26.

    84. A. Rafiq, M. Rafiullah, Some multi-step iterative methods for solving nonlinear equations, Computers & Mathematics with Applications 58 (8) ( 2009), 1589-1597.

    85. A. Rafiq, Fixed point iterations of two asymptotically pseudocontractive mappings, Bulletin of the Allahabad Mathematical Society (2010), in press.

    86. A. Rafiq, On three-step iterative process for asymptotically nonexpansive mappings, Indain Journal of Mathematics (2010), in press.

    87. A. Rafiq, A. M. Acu, F. Sofonea, On weighted Cebysev inequalities, The Land Forces Academy Review 2 (54) (2009), 79-84.

    88. F. Ahmad, N. A. Mir, A. Rafiq, weighted cebysev type inequalities involving functions whose first derivatives belong to Lp(a,b), Kragujevac J. Math. 32 (2009), 13-26.

    89. Lj. B. Ciric, B. S. Lee, A. Rafiq, Three-step steepest descent approximations in Banach spaces, Nonlinear Analysis Forum 14 (2009), 63-72.

    90. A. Rafiq, B. S. Lee, An implicit iteration process for a finite family of strongly pseudocontractive mappings, J. Korean Soc. Math. Ser. B: Pure Appl. Math. 16 (3) (2009), 307-314.

    91. A. Rafiq, B. S. Lee, A note on “Simpler is also better in approximating fixed points”, Nonlinear Analysis Forum 14 (2009), 99-102.

    92. B. S. Lee, A. Rafiq, Fixed point iterations for a family of asymptotically pseudocontractive mapping, Nonlinear Analysis Forum 14 (2009), 63-72.

    93. A. Rafiq, A. M. Acu, F. Sofonea, An iterative algorithm for two asymptotically pseudocontractive mappings, Int. J. Open Problems Compt. Math. 2 (3) (2009), 372-382.

    94. A. Rafiq, Fixed point iterations of three asymptotically pseudocontractive mappings, Demonstratio Mathematica (2010), in press.

    95. A. Rafiq, R. A. Rashwan, Approximation schemes for the fixed points of finite family of asymptotically pseudocontractive mappings, General Mathematics (2009), inpress.

    96. A. Rafiq, On multi-step approximation schemes for the fixed Points of asymptotically pseudocontrative mappings, Indian Journal of Mathematics (2010), in press.

    97. A. Rafiq, On asymptotically pseudocontractive mappings, Journal of Nonlinear Functional Analysis and Applications (2010), in press.

    98. A. Rafiq, Convergence theorems for uniformly L-lipschitzian asymptotically nonexpansive mappings, Acta Universitatis Apulensis 20 (2010), in press.

    99. F. Ahmad, S. Hussain, N. A. Mir, A. Rafiq, New sixth order Jarratt method for solving nonlinear equations, Int. J. of Appl. Math. and Mech. 5 (5) (2009), 27-35.

    100. A. Rafiq, Some results on asymptotically pseudocontractive mappings, Fixed Point Theory (2010), in press.

    101. A. M. Acu, A. Rafiq, C. V. Muraru, The remainder term of some quadrature formulae, Studii şi Cercetari Ştiinţifice, Seria Matematica, Bacău (2009), in press.

    102. A. Rafiq, Q. Shahbaz, A. M. Acu, The Generalized Cebysev type inequality, Studii şi Cercetari Ştiinţifice, Seria Matematica, Bacău (2009), in press.

    103. A. M. Acu, A. Rafiq, F. Sofonea, Some new four-point quadrature formulas, Analele Stiintifice ale Universitatii Ovidius Constanta 17 (3) (2009), 1-13.

    Papers presented at Conferences

    1. A. M. Acu, M. Acu, A. Rafiq, Some inequalities of Ostrowski type in the case of weighted integrals, Proceedings of the Fifth International Symposium "Mathematical Inequalities" Sibiu-Romania (2008), ISBN 978-973-739-740-9, 9-22.

    2. F. Sofonea, A. M. Acu, A. Rafiq, An error analysis for a family of four-point quadrature formulas, Proceedings of the Fifth International Symposium "Mathematical Inequalities" Sibiu-Romania (2008), ISBN 978-973-739-740-9, 136-145.

    3. M. Acu, A. Rafiq, About a linear positive functional, Proceedings of the 12th Symposium of Mathematics and its Applications, "Politehnica" University of Timisoara (2009).

    Reviewer of the following International Journals

    1. Zentralblatt MATH.
    2. International Journal of Computer Mathematics.
    3. Applied Mathematics and Computation.
    4. Journal of Computational and Applied Mathematics.
    5. Mathematical and Computer Modeling.
    6. Physics Letters A.
    7. Fixed Point Theory and Applications.
    8. Journal of Inequalities and Applications.
    9. Kuwait Journal of Science and Engineering.
    10. Applied Mathematics Electronic Notes.
    11. IEEE Society.
    12. Journal of Applied Analysis.
    13. Mathematical Communications,
    14. Indian Journal of Mathematics.
    15. Bulletin of AMS.
    16. DEMONSTRATIO MATHEMATICA.
    17. Proceedings of the Pakistan Academy of Sciences.
    18. Fixed Point Theory.
    19. Banach Journal of Mathematical Analysis.
    20. Journal of Applied Mathematics and Computing.
    21. BULLETIN of the Malaysian Mathematical Sciences Society.
    22. World Applied Sciences Journal.
    23. Journal of Advanced Research in Pure Mathematics.
    24. Mathematical Modeling and Analysis.
    25. Applicable Analysis and Discrete Mathematics.
    26. Annales Mathematicae et Informaticae.
    27. Computers and Mathematics with Applications.