Afrika Matematika https://doi.org/10.1007/s13370-018-0613-1 New generalized system of variational inclusions involving H(·, ·)-co-accretive mapping Mohd. Akram 1 · Mohd. Dilshad 2 Received: 24 January 2016 / Accepted: 18 July 2018 © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018 Abstract The aim of this paper is to study a new generalized system of nonlinear variational inclusions involving H (·, ·)-co-accretive mapping in Banach spaces. Using the concept of resolvent operator associated to H (·, ·)-co-accretive mapping, we prove the existence for this general- ized system of nonlinear variational inclusions. We show the convergence and stability of this new system of variational inclusion using the proposed perturbed iterative algorithm. The results presented in this paper generalize, improve and unify the previously known results in this area. An example is also given. Keywords Convergence · H (·,·)-co-accretive mapping · Perturbed iterative algorithm · System of variational inclusions Mathematics Subject Classification 47H09 · 49J40 1 Introduction In the last two decades, variational inclusions, generalized forms of variational inequalities have been extensively studied and generalized in various directions to study a wide class of problems arising in mechanics, economics, optimizations, nonlinear programming problems, finance and applied sciences. One of the important and most interesting aspects of the theory of variational inclusions is to develop an efficient and implementable iterative algorithm to compute the approximate solution of a variational inclusion. Fang and Huang [4], introduced a new class of H -accretive operators in Banach spaces and extend the concept of resolvent operators associated with classical m-accretive oper- ators to new H -accretive operators. After that Fang and Huang [5], Fang et al. [6] and B Mohd. Akram akramkhan_20@rediffmail.com Mohd. Dilshad mdilshaad@gmail.com 1 Department of Mathematics, Faculty of Science, Islamic University in Madinah, Madinah 170, Kingdom of Saudi Arabia 2 Department of Mathematics, University of Tabuk, Tabuk 71491, Kingdom of Saudi Arabia 123