%0 Journal Article
%T $H(.,.,.,.)$-$\varphi$-$\eta$-cocoercive Operator with an Application to Variational Inclusions
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Ram, Tirth
%A Iqbal, Mohd
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 1311-1327
%! $H(.,.,.,.)$-$\varphi$-$\eta$-cocoercive Operator with an Application to Variational Inclusions
%K Variational-like inclusions
%K co-corecive operator
%K Semi-inner product spaces
%K Resolvent operator
%K Lipschitz continuity
%R 10.22075/ijnaa.2021.23245.2506
%X In this work, we study generalized $ H(.,.,.,.)$-$\varphi$-$\eta-$ cocoercive operator to find the solution of variational like inclusion involving an infinite family of set-valued mappings in semi-inner product spaces via resolvent equation approach. Furthermore, we established an equivalence between the set-valued variational-like inclusion problem and fixed point problem by employing generalized resolvent operator technique involving generalized $H(.,.,.,.)$-$\varphi$-$\eta$-cocoercive operator. Using the equivalent formulation of set-valued variational-like inclusion problem and resolvent equation problem, an iterative algorithm is developed that approximate the uniqueness of solution of the resolvent equation problem.
%U https://ijnaa.semnan.ac.ir/article_5693_08c18ebff883dd381a74af1baf6d3bfb.pdf