SỰ HỘI TỤ MẠNH CỦA DÃY LẶP LAI GHÉP CÓ YẾU TỐ QUÁN TÍNH CHO HAI ÁNH XẠ G-KHÔNG GIÃN TIỆM CẬN TRONG KHÔNG GIAN HILBERT VỚI ĐỒ THỊ

Abstract

          In this paper, by combining the shrinking projection method with a modified inertial S-iteration process, we introduce a new inertial hybrid iteration for two asymptotically G-nonexpansive mappings and a new inertial hybrid iteration for two G-nonexpansive mappings in Hilbert spaces with graphs. We establish asufficient condition for the closedness and convexity of the set of fixed points of asymptotically G-nonexpansive mappings in Hilbert spaces with graphs. We then prove a strong convergence theorem for finding a common fixed point of two asymptotically G-nonexpansive mappings in Hilbert spaces with graphs. By this theorem, we obtain a strong convergence result for two G-nonexpansive mappings in Hilbert spaces with graphs. These results are generalizations and extensions of some convergence results in the literature, where the convexity of the set of edges of a graph is replaced by coordinate-convexity. In addition, we provide a numerical example to illustrate the convergence of the proposed iteration processes.    

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