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In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and q -uniformly smooth real Banach spaces ( q > 1 ). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space l 4 (R) to study the effect of the relaxation and inertial parameters in our proposed algorithm. In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and -uniformly smooth real Banach spaces ( ). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space to study the effect of the relaxation and inertial parameters in our proposed algorithm. [ABSTRACT FROM AUTHOR]

The proximal point algorithm (PPA) is a powerful tool for solving monotone inclusion problems. Recently, Tao and Yuan [On the optimal linear convergence rate of a generalized proximal point algorithm, J. Sci. Comput. 74 (2018), 826-850] proposed a generalized PPA (GPPA) for finding a zero point of a maximal monotone operator, and obtained the linear convergence rate of the generalized PPA. In this paper, we consider accelerating the GPPA with the aid of the inertial extrapolation. We propose a generalized proximal point algorithm with alternating inertial steps solving monotone inclusion problem, and obtain weak convergence results under some mild conditions. When the inverse of the involved monotone operator is Lipschitz continuous at the origin, we prove that the iterative sequence generated by our generalized proximal point algorithm is linearly convergent. The Fej'er monotonicity of even subsequences of the iterative sequence is also recovered. Finally, we give some priori and posteriori error estimates of our generated sequences. [ABSTRACT FROM AUTHOR]