The Existence and Approximation Fixed Point Theorems for Monotone Nonspreading Mappings in Ordered Banach Spaces

Khanitin Muangchoo-in, Poom Kumam


In this paper, we proved some existence theorems of fixed points for monotone nonspreading mappings \(T\) in a Banach space \(E\) with the partial order \(\leq\). In order to finding a fixed point of such a mapping \(T\), moreover we proved the convergence theorem of Mann iterative schemes under the condition \(\sum\limits_{n=1}^\infty\beta_n(1-\beta_n)=\infty\), which contain \(\beta_n=\frac1{n+1}\) as a special case.


Ordered Banach space; Fixed point; Monotone nonspreading mapping; Mann iterative scheme

Full Text:



M. Bachar and M. A. Khamsi, Fixed points of monotone mappings and application to integral equations, Fixed Point Theory Appl. 2015 (2015), 110, DOI: 10.1186/s13663-015-0362-x.

B. A. B. Dehaish, M. A. Khamsi, Mann iteration process for monotone nonexpansive mappings, Fixed Point Theory Appl. 2015 (2015), 177, DOI: 10.1186/s13663-015-0416-0.

F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings relate to maximal monotone operators in Banach spaces, Arch. Math. (Basel) 91 (2008), 166 – 177, DOI: 10.1007/s00013-008-2545-8.

L. S. Liu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114 – 125, DOI: 10.1006/jmaa.1995.1289.

W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506 – 510, DOI: 10.1090/S0002-9939-1953-0054846-3.

E. Naraghirad, On an open question of Takasashi for nonpsreading mapping in Banach spaces, Fixed Point Theory Appl. 2013 (2013), 228, DOI: 10.1186/1687-1812-2013-228.

Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 591 – 597, DOI: 10.1090/S0002-9904-1967-11761-0.

W. Takahashi, Nonlinear Functional Analysis – Fixed Point Theory and its Applications, Yokohama Publishers Inc., Yokohama (2000).

H. K. Xu, Inequality in Banach spaces with applications, Nonlinear Anal. 16 (1991), 1127 – 1138, DOI: 10.1016/0362-546X(91)90200-K.

H. Zhang and Y. Su, Convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces, Nonlinear Anal. 71 (2009), 4572 – 4580, DOI: 10.1016/

H. Zhou, Convergence theorems for ¸-strict pseudo-contractions in 2-uniformly smooth Banach spaces, Nonlinear Anal. 69 (2008), 3160 – 3173, DOI: 10.1016/


eISSN 0975-5748; pISSN 0974-875X