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Abstract
In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition
Highlights
A2 andH2 as a bounded linear operator having A∗ as the adjoint operator of A
In this paper, a new iterative scheme is introduced and strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented
Using the CQ-algorithm for solving the split feasibility problem (SFP) (2), in 2002 Byrne [2] proposed that which generates the new iterate as follows choosing arbitrarily x1 ∈ H1, xn+1 = PC[xn − γAT (I − PQ)Axn]
Summary
H2 as a bounded linear operator having A∗ as the adjoint operator of A. In 2012, Chang et al [9] again, using (10) proved the weakly convergence of the sequence {xn} to the split common fixed point x∗ ∈ Γ of asymptotically quasi-nonexpansive mapused to obtain the strong convergence for SCFPP (6) in uniformly convex and uniformly smooth Banach spaces, without the assumption of semi-compactness property and or without ping in Hilbert spaces. These authors could only obtain the assumption of Opial condition. In 2015, Zhang et al [10] introduced the iterative scheme which guarantees the strong converges for SCFP of the asymptotically nonexpansive mapping in Hilbert spaces, without as-
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