Filomat 2023 Volume 37, Issue 19, Pages: 6255-6275
https://doi.org/10.2298/FIL2319255G
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Approximating solutions of general class of variational inclusions involving generalized αiβj-(Hp,φ)-η-accretive mappings
Gupta Sanjeev (Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura, India), guptasanmp@gmail.com
Rathour Laxmi (Ward Number, Bhagatbandh, Anuppur, India), laxmirathour817@gmail.com
The present research is an attempt to define a class of generalized
αiβj-(Hp,φ)-η-accretive mappings as well as it is a study of its associated
class of proximal-point mappings. The generalized αiβj-(Hp,φ)-η-accretive
mappings is the sum of two symmetric accretive mappings and an extension of
the generalized αβ-H(.,.)-accretive mapping [28]. Further the research is a
discussion on graph convergence of generalized αiβj-(Hp,φ)-η-accretive
mappings and its application includes a set-valued variational-like
inclusion problem (SVLIP, in short) in semi inner product spaces.
Furthermore an iterative algorithm is proposed, and an attempt is made to
discuss the convergence analysis of the sequences generated from the
proposed iterative algorithm. An example is constructed that demonstrate few
graphics for the convergence of proximal-point mapping. Our results can be
viewed as a refinement and generalization of some known results in the
literature.
Keywords: Generalized αiβj-(Hp, φ)-η-accretive mappings, proximal point mapping, graph convergence, iterative algorithms, variational-like inclusions, semi inner product spaces
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