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Keywords = generalized αiβj-Hp(., ., ...)-accretive mappings

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15 pages, 318 KiB  
Article
Set-Valued Variational Inclusion Governed by Generalized αiβj-Hp(., ., ...)-Accretive Mapping
by Sanjeev Gupta and Faizan Ahmad Khan
Axioms 2022, 11(10), 539; https://doi.org/10.3390/axioms11100539 - 8 Oct 2022
Cited by 4 | Viewed by 1416
Abstract
This work is concerned with the new notion called generalized αiβj-Hp(., ., ...)-accretive mapping that is the sum of two symmetric accretive mappings. It is an extension [...] Read more.
This work is concerned with the new notion called generalized αiβj-Hp(., ., ...)-accretive mapping that is the sum of two symmetric accretive mappings. It is an extension of the generalized αβ-H(., .)-accretive mapping. The proximal point mapping linked to the generalized αiβj-Hp(., ., ...)-accretive mappings is defined, and some of its characteristics are discussed. As an application of the new proximal point mapping, we consider a set-valued variational inclusion problem in q-uniformly smooth Banach spaces. Further, we propose an iterative scheme connected with αiβj-Hp(., ., ...)-proximal point mapping to find the solution of a variational inclusion problem and discuss its convergence criteria under appropriate assumptions. Some examples are constructed in support of generalized αiβj-Hp(., ., ...)-accretive mappings. Full article
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