Geodesic
A class of Yosida inclusion and graph convergence on Yosida approximation mapping with an application
Filomat, Tome 37 (2023) no. 15, p. 4881

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DOI

The proposed work is presented in two folds. The first aim is to deals with the new notion called generalized αiβ j-Hp(., ., ...)-accretive mappings that are the sum of two symmetric accretive mappings. It is an extension of αβ-H(., .)-accretive mapping, studied and analyzed by Kazmi [18]. We define the proximal- point mapping associated with generalized αiβ j-Hp (., .,...)-accretive mapping and demonstrate aspects on single-valued property and Lipschitz continuity. The graph convergence of generalized αiβ j-Hp(., ., ...)- accretive mapping is discussed. Second aim is to introduce and study the generalized Yosida approximation mapping and Yosida inclu- sion problem. Next, we obtain the convergence on generalized Yosida approximation mappings by using the graph convergence of generalized αiβ j-Hp(., ., ...)-accretive mappings without using the convergence of its proximal-point mapping. As an application, we consider the Yosida inclusion problem in q-uniformly smooth Banach spaces and propose an iterative scheme connected with generalized Yosida approximation mapping of generalized αiβ j-Hp(., ., ...)-accretive mapping to find a solution of Yosida inclusion problem and discuss its convergence criteria under appropriate assumptions. Some examples are constructed and demonstrate few graphics for the convergence of proximal-point mapping as well as generalized Yosida approximation mapping linked with generalized αiβ j-Hp(., ., ...)-accretive mappings.
DOI : 10.2298/FIL2315881G
Classification : 49J40, 47H19
Keywords: Generalized αiβ j-Hp(., ., ...)-accretive mappings, Yosida approximation mapping, Proximal-point mapping, Graph convergence, Iterative algorithm, Variational inclusion 
Sanjeev Gupta; Faizan Ahmad Khan. A class of Yosida inclusion and graph convergence on Yosida approximation mapping with an application. Filomat, Tome 37 (2023) no. 15, p. 4881 . doi: 10.2298/FIL2315881G
@article{10_2298_FIL2315881G,
     author = {Sanjeev Gupta and Faizan Ahmad Khan},
     title = {A class of {Yosida} inclusion and graph convergence on {Yosida} approximation mapping with an application},
     journal = {Filomat},
     pages = {4881 },
     year = {2023},
     volume = {37},
     number = {15},
     doi = {10.2298/FIL2315881G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2315881G/}
}
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