A common solution of f-fixed point and variational inequality problems in Banach spaces

Optimization ◽  
2021 ◽  
pp. 1-26
Author(s):  
Habtu Zegeye ◽  
Oganeditse A. Boikanyo
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Banach Spaces ◽  
Variational Inequality Problems ◽  
Common Solution

scholarly journals Strong convergence theorems for variational inequalities and fixed point problems in Banach spaces

2021 ◽  
Vol 37 (3) ◽  
pp. 477-487
Author(s):  
MONDAY OGUDU NNAKWE ◽  
◽  
" JERRY N." EZEORA ◽  
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Projection ◽  
Finite Family ◽  
Common Solution ◽  
Monotone Type

In this paper, using a sunny generalized non-expansive retraction which is different from the metric projection and generalized metric projection in Banach spaces, we present a retractive iterative algorithm of Krasnosel’skii-type, whose sequence approximates a common solution of a mono-variational inequality of a finite family of η-strongly-pseudo-monotone-type maps and fixed points of a countable family of generalized non-expansive-type maps. Furthermore, some new results relevant to the study are also presented. Finally, the theorem proved complements, improves and extends some important related recent results in the literature.

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