STRONG CONVERGENCE OF EXTENDED GENERAL VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS

摘要: Abstract. In this paper, we suggest and analyze some three step itera-tive scheme for nding the common elements of set solutions ofthe extended general variational inequalities involving operators andthe xed points nonexpansive mappings. We also considerthe convergence analysis suggested iterative schemes under mildconditions. Since includegeneral several other classes in-equalities as special cases, results obtained in paper continue to holdfor these problems. Results may be viewed are nement improvement previously known results. 1. IntroductionThroughout assume that H is a real Hilbert space, whoseinner product norm denoted by h;iand kkrespectively. Let Kbenonempty closed convex H, T;g;h: H!Hbe given nonlinearoperators. consider problem u2H;h(u) 2Ksuch thathTu;g(v) h(u)i0; 8v2H;g(v) 2K: (1:1)An inequality type (1.1) called in-volving operators, which was introduced studied Noor [2]. Onecan show provide us uni- ed, simple, natural framework study wide class problemswhich arise various areas pure applied sciences. Using projectiontechnique, [2] established equivalence between