We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvaluetype qua...

The operator B in a complex Hubert space H is said to form an angle Θ with the (stronger) operator A if D(A) c D(B) and, for every x in D(A), (Ax, Bx)π belongs to the cone K(θ) of all complex z with | arg (z) \ ̂ θ. If A and I? are closed maximal accretive operators and B forms a right angle with A, then A + JE> is closed maximal accretive and the Cauchy problem for each of the equations u(t) -f...

In the sequel, we shall denote the single-valued normalized duality map by j. Let F (T ) = {x ∈ E : Tx = x} denote the set of all fixed point for a mapping T . We write xn ⇀ x (respectively xn ∗ ⇀ x) to indicate that the sequence xn weakly (respectively weak∗) converges to x; as usual xn → x will symbolize strong convergence. A mapping A : D(A) ⊂ E → 2 is called to be accretive if for all x, y ...

The purpose of this paper is to introduce and study a new kind of generalized strongly nonlinear operator inclusion problems involving generalized m-accretive mapping in Banach spaces. By using the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang, we also prove the existence theorem of the solution for this kind of operator inclusion problems and construct ...

We study a new system of nonlinear set-valued variational inclusions involving a finite family of H ·, · -accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of H ·, · -accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme...

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

This paper is dedicated to study a new class of general nonlinear random A-maximal m-relaxed η-accretive (so called (A, η)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal m-relaxed η-accretive mappings due to Lan et al. and Chang’s lemma [13], some new ite...

We use Nadler’s theorem and the resolvent operator technique for m-accretive mappings to suggest an iterative algorithm for solving generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces. We prove the existence of solutions for our inclusions without compactness assumption and the convergence of the iterative sequences generated by the algorithm i...

* Correspondence: [email protected] Department of Mathematics, Sichuan University of Science and Engineering, Zigong, 643000, Sichuan, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we develop a new perturbed iterative algorithm framework with errors based on the variational graphical convergence of operator sequences w...

In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...