In order to solve issues that arise in various branches of mathematical analysis, such as split feasibility problems, variational inequality nonlinear optimization issues, equilibrium complementarity selection and matching proving the existence solutions integral differential equations, fixed point theory provides vital tools. this study, we discuss topological structure several fixed-point the...

We present a new sufficient condition under which a maximal monotone operator T : X ⇉ X∗ admits a unique maximal monotone extension to the bidual T̃ : X∗∗ ⇉ X∗. For non-linear operators this condition is equivalent to uniqueness of the extension. The class of maximal monotone operators which satisfy this new condition includes class of Gossez type D maximal monotone operators, previously defined...

In this paper we analyze the problem of checking whether a default theory has a single extension. This problem is important for at least three reasons. First, if a theory has a single extension, nonmonotonic inference can be reduced to entailment in propositional logic (which is computationally easier) using the set of consequences of the generating defaults. Second, a theory with many extensio...

Let D be an unbounded domain in R with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x)dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r...

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

In formal argumentation, grounded semantics is well known for yielding exactly one unique extension. Since grounded semantics has a very sceptical nature, one can ask the question whether it is possible to define a unique extension semantics that is more credulous. Recent work of Dung, Mancarella and Toni proposes what they call ideal semantics, which is a unique extension semantics that is mor...

objectives this study aimed at reviewing the current literature on the diagnosis, staging, and different treatment strategies for wilms’ tumor with either ureteral or intravascular extension. evidence acquisition in this article, we reviewed the current literature about staging, diagnosis, and management strategies for wt, through a randomized clinical trial, which focused on this matter. the m...