A Self-Adaptive Algorithm for Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings

2020 ◽  
Vol 170 (1) ◽  
pp. 883-901
Author(s):  
Suthep Suantai ◽  
Pachara Jailoka
Keyword(s):  
Fixed Point ◽  
Adaptive Algorithm ◽  
Null Point ◽  
Fixed Point Problems ◽  
Multivalued Mappings ◽  
Demicontractive Multivalued Mappings ◽  
Self Adaptive

scholarly journals A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2039 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Adaptive Method ◽  
Convergence Result ◽  
Null Point ◽  
Fixed Point Problems ◽  
Bounded Linear ◽  
Contraction Method ◽  
Projection And Contraction Method ◽  
Self Adaptive

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods.

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