Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301$H(.,.,.,.)$-$\varphi$-$\eta$-cocoercive Operator with an Application to Variational Inclusions13111327569310.22075/ijnaa.2021.23245.2506ENTirth RamDepartment of Mathematics, University of Jammu, Jammu-180006, India0000-0002-6447-6767Mohd IqbalDepartment of Mathematics, University of Jammu, Jammu-180006, India0000-0002-3269-9333Journal Article20210425In 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.https://ijnaa.semnan.ac.ir/article_5693_08c18ebff883dd381a74af1baf6d3bfb.pdf