Perturbed algorithms for solving nonlinear relaxed cocoercive operator equations with general A-monotone operators in Banach spaces |
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| Affiliation: | 1. Department of Computer Science, Sichuan University of Sciences & Engineering, Zigong, Sichuan 643000, PR China;2. Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, PR China;3. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;1. LATP, CMI, 39 rue F. Joliot-Curie, 13453 Marseille, France;2. IML, Luminy, case 907, 13288 Marseille Cedex, France;1. Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Naukova Street 3 B, Lviv 79060, Ukraine;2. SGT Inc., 7701 Greenbelt Rd Suite 400 Greenbelt, MD 20770, USA;3. NASA Ames Research Center, Moffett Field, CA 94035-1000, USA |
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| Abstract: | Based on the notion of general A-monotonicity, the new proximal mapping technique and Alber’s inequalities, a new class of nonlinear relaxed cocoercive operator equations with general A-monotone operators in Banach spaces is introduced and studied. Further, we also discuss the convergence and stability of a new perturbed iterative algorithm with errors for solving this class of nonlinear operator equations in Banach spaces. Since general A-monotonicity generalizes general H-monotonicity (and in turn, generalizes A-monotonicity, H-monotonicity and maximal monotonicity), our results improve and generalize the corresponding results of recent works. |
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