In this paper, a new system of nonlinear set-valued variational inclusions involving (H, η)-monotone mappings in Hilbert spaces is introduced and studied. By using the resolvent operator method associated with (H, η)-monotone mappings, an existence theorem of solutions for this kind of system of nonlinear set-valued variational inclusion is established and a new iterative algorithm is suggested...

Protein-DNA bindings are essential activities. Understanding them forms the basis for further deciphering biological and genetic systems. In particular, the proteinDNA bindings between Transcription Factors (TFs) and Transcription Factor Binding Sites (TFBSs) play a central role in gene transcription. Comprehensive TF-TFBS binding sequence pairs have been found in a recent study. However, they ...

in this paper, we prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. to prove the theorem, we use a non compatible condition, that is, weak commutativity of type (kb). we show that completeness of the whole space is not necessary for the existence and uni...

This work aims to develop a new class of accretive mappings and investigate its associated proximal mappings. is known as generalized (Hk,φ)-η-accretive Further, the research includes discussion application, leading set-valued variational-like inclusions (SVVLI, in short) semi-inner product spaces. The corresponding fixed point problem for SVVLI given. used provide an iterative scheme solving S...

Abstract In this paper, we deal with perturbations of two general functional equations in several variables. Namely, prove the generalized, spirit Bourgin, Ulam stability these Banach spaces. order to do this, use fixed point method. Moreover, as corollaries from our main results, get outcomes on approximate solutions a few important classic equations. They include, among others, which characte...

We consider an approach to constructing a non-anticipating selection of a multivalued mapping; such a problem arises in control theory under conditions of uncertainty. The approach is called “unlocking of predicate” and consists in the reduction of finding the truth set of a predicate to searching fixed points of some mappings. Unlocking of predicate gives an extra opportunity to analyze the tr...

F(T) ̸ = 0. As an important generalization of nonexpansive mappings, the class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] in 1972, who proved that if K is a nonempty, closed, and convex subset of a real uniformly convex Banach space and T : K → K is an asymptotically nonexpansive mapping, then T has a fixed point. Since then, iterative techniques for approximat...

Mapping of mutations on a phylogeny has been a commonly used analytical tool in phylogenetics and molecular evolution. However, the common approaches for mapping mutations based on parsimony have lacked a solid statistical foundation. Here, I present a Bayesian method for mapping mutations on a phylogeny. I illustrate some of the common problems associated with using parsimony and suggest inste...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.