Convergence of SP-iteration for generalized nonexpansive mapping in Banach spaces

  • J. Ali Dep. Math., Aligarh Muslim Univ., India
  • I. Uddin Dep. Math., Jamia Millia Islamia, New Delhi, India
Keywords: Banach spaces, Fixed point, Weak-convergence, condition (C) and Opial’s property


UDC 517.9

Phuengrattana and Suantai [J. Comput. and Appl. Math., 235, 3006 – 3014 (2011)] introduced an iteration scheme and they named this iteration as SP-iteration. In this paper, we study the convergence behaviour of SP-iteration scheme for the class of generalized nonexpansive mappings. One weak convergence theorem and two strong convergence theorems in uniformly convex Banach spaces are obtained. We also furnish a numerical example in support of our main result. In process, our results generalize and improve many existing results in the literature.


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How to Cite
Ali, J., and I. Uddin. “Convergence of SP-Iteration for Generalized Nonexpansive Mapping in Banach Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 6, June 2021, pp. 738 -48, doi:10.37863/umzh.v73i6.350.
Research articles