We prove path convergence theorems and introduce a new iterative sequence for a countably infinite family of m-accretive mappings and prove strong convergence of the sequence to a common zero of these operators in uniformly convex real Banach space. Consequently, we obtain strong convergence theorems for a countably infinite family of pseudocontractive mappings. Our theorems extend and improve ...

Based on the notion of (A,η)-accretive mappings and the resolvent operators associated with (A,η)-accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problemswith (A,η)-accretivemappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving (A,η)-ac...

Let A be a positive self-adjoint operator and let B be an m-accretive operator which is A-small with a relative bound less than one. Let H = A + B, then H is well-deened on dom(H) = dom(A) and m-accretive. If B is a strictly m-accretive operator obeying dom((H)) dom(A) \ dom((B)) 6 = f0g for some 2 (0; 1]; (1) then for the Trotter product formula we prove that ?

μ1(T) measures the maximum turning capability of T . A vector f for which the inf in (1.1) is attained is called an antieigenvector of T . Cosine of T has important applications in pure operator theory as well as numerical analysis (see [3, 4, 6]). In [7, 8, 11], we have computed the first antieigenvalue of normal accretive operators in terms of eigenvalues of these operators. In [12], we compu...

In the paper we provide construction of a coincidence degree being homotopy invariant detecting existence solutions equations or inclusions form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an $m$-accretive operator in Banach space $ E$, $F\colon K\multimap weakly upper semicontinuous set-valued map constrained to open subset $U$ closed set $K\subset E$. Two different approaches w...

We introduce and study a new system of variational inclusions with (H ,η)-accretive operators, which contains variational inequalities, variational inclusions, systems of variational inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (H ,η)-accretive operators, we prove the existence and uniqueness of solution and the...