$H(.,.,.,.)$-$\varphi$-$\eta$-cocoercive Operator with an Application to Variational Inclusions

	$H(.,.,.,.)$-$\varphi$-$\eta$-cocoercive Operator with an Application to Variational Inclusions
International Journal of Nonlinear Analysis and Applications
مقاله 110، دوره 13، شماره 1، خرداد 2022، صفحه 1311-1327 اصل مقاله (400.91 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23245.2506
نویسندگان
Tirth Ram^* ؛ Mohd Iqbal
Department of Mathematics, University of Jammu, Jammu-180006, India
چکیده
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.
کلیدواژه‌ها
Variational-like inclusions؛ co-corecive operator؛ Semi-inner product spaces؛ Resolvent operator؛ Lipschitz continuity
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