Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces

In this work, we introduce two modified Tseng's splitting algorithms with a new non-monotone adaptive step size for solving monotone inclusion problem in the framework of Banach spaces. Under some mild assumptions, we establish the weak and strong convergence results of the proposed algorithms. Moreover, we also apply our results to variational inequality problem, convex minimization problem and signal recovery, and provide several numerical experiments including comparisons with other related algorithms. Keywords: maximal monotone operator; Banach space; strong convergence; self adaptive method Mathematics Subject Classification: 47H09, 47H10, 47J25