General strongly nonlinear variational inequalities

Strong Convergence Theorems for a Generalized Equilibrium Problem with a Relaxed Monotone Mapping and a Countable Family of Nonexpansive Mappings in a Hilbert Space

“…In the case of η x, y x − y for all x, y ∈ C, T is said to be relaxed α-monotone. In the case of η x, y x − y for all x, y ∈ C and α z k z p , where p > 1 and k > 0, T is said to be p-monotone; see [11][12][13] . In fact, in this case, if p 2, then T is a k-strongly monotone mapping.…”

A Perturbated Algorithm for Generalized Nonlinear Quasi-Variational Inclusions

“…Then we prove the convergence of this algorithm, by using the definition of multi-valued relaxed Lipschitz operators. Our result is more general than the one considered in [3,4,5,6,8,9,10] which motivated us for the present work. …”

“…Finally, we obtain the perturbed algorithm which generates from any starting point Xo in H a sequence {xn} by the rule our algorithm (3.4) is more general than the algorithms considered by Hassouni and Moudafi [4], Noor [6]and Siddiqi and Ansari [8].…”

“…II. Let for the appropriate suitable choice of operators T, f, 9 and m, includes many kinds of variational inequalities and quasi-variational inequalities of [4,6,8,9,10], as special cases.…”

On convergence of random iterative schemes with errors for strongly pseudo-contractive Lipschitzian maps in real Banach spaces

“…The machinery of fixed point theory provides a convenient way of modelling many problems arising in non-linear analysis, probability theory and for a solution of random equations in applied sciences, see [4,9,11,12,15,17,18,20,21,25,27,29,30,31,33,34,35,36,38,39,40] and references there. With the developments in random fixed point theory, there has been a renewed interest in random iterative schemes [2,3,7,8,10].…”