THE CONVERGENCE OF MODIFIED MANN ITERATIVE SCHEME WITH WEAKLY CONTRACTIVE CONDITION
Keywords:
modified Mann iterative scheme, weakly contractive mapping, common fixed pointAbstract
In this paper, we study the convergence of a sequence, which is modified from Mann iterative scheme, with a weakly contractive mapping condition. The convergence of two sequences which are generalized from the modified Mann iterative scheme are also considered. Furthermore, we show that these sequences converge to a common fixed point. Our results generalize and extend various known results in the literature.
References
Abbas M, Khan MA. Common fixed point theorem of two mappings satisfying a generalized weak contractive condition, International Journal of Mathematics and Mathematical Sciences. 2009; 9.
Ahmed MA. Common fixed point theorems for weakly compatible mapping. The Rocky Mountain Journal of Mathematics. 2003; 33(4): 1189-1203.
Alber YI. Guerre-Delabriere S. Principle of weakly contractive maps in Hilbert spaces, New Results in Operator Theory and Its Applications (I. Gohberg and Yu. Lyubich, eds.), Operator Theory Advance Applications. 1997; 98: 7-22.
Banach S. Sur les operation danslesensemblesabstraitsetleur application aux eqeations integrals. Fundamenta Mathematicae. 1922; 3: 133-181.
Beg I, Abbas M. Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory and Applications. 2006; 1–7.
Chang SS. The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings, Computers & Mathematics with Applications. 1999; 37(9): 17-24.
Hicks T L, Kubicek JR. On the Mann iteration process in Hilbert space, Journal of Mathematical Analysis and Applications. 1979; 59: 498-504.
Jungck G. Common fixed point for commuting and compatible maps on compacta, Proceedings of the American Mathematical Society. 1988; 103(3): 977-983.
Kreyszig E. Introductory Functional Analysis with Applications. JonhWiley & Sons, 1989.
Rhoades BE. Some theorems on weakly contractive maps, Nonlinear Analysis. 2001; 47(4): 2683-2693.
Ahmed MA. Common fixed point theorems for weakly compatible mapping. The Rocky Mountain Journal of Mathematics. 2003; 33(4): 1189-1203.
Alber YI. Guerre-Delabriere S. Principle of weakly contractive maps in Hilbert spaces, New Results in Operator Theory and Its Applications (I. Gohberg and Yu. Lyubich, eds.), Operator Theory Advance Applications. 1997; 98: 7-22.
Banach S. Sur les operation danslesensemblesabstraitsetleur application aux eqeations integrals. Fundamenta Mathematicae. 1922; 3: 133-181.
Beg I, Abbas M. Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory and Applications. 2006; 1–7.
Chang SS. The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings, Computers & Mathematics with Applications. 1999; 37(9): 17-24.
Hicks T L, Kubicek JR. On the Mann iteration process in Hilbert space, Journal of Mathematical Analysis and Applications. 1979; 59: 498-504.
Jungck G. Common fixed point for commuting and compatible maps on compacta, Proceedings of the American Mathematical Society. 1988; 103(3): 977-983.
Kreyszig E. Introductory Functional Analysis with Applications. JonhWiley & Sons, 1989.
Rhoades BE. Some theorems on weakly contractive maps, Nonlinear Analysis. 2001; 47(4): 2683-2693.
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Published
2018-08-30
How to Cite
Tangkhawiwetkul, J., & Songnon, P. (2018). THE CONVERGENCE OF MODIFIED MANN ITERATIVE SCHEME WITH WEAKLY CONTRACTIVE CONDITION. Life Sciences and Environment Journal, 19(2), 243–250. retrieved from https://ph01.tci-thaijo.org/index.php/psru/article/view/84789
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