In this paper, coupled xed point results of Bhaskar-Lakshmikantham type [T. Gnana Bhaskar, V.Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, NonlinearAnalysis 65 (2006) 1379-1393] are extend, generalized, unify and improved by using monotonemappings instead mappings with mixed monotone property. Also, an example is given to supportthese improvements.

In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean, and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in commutative, free and Boolean cases. The way we define (generalized) cumulants ...

The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this pa...

We extend the Malitsky-Tam forward-reflected-backward (FRB) splitting method for inclusion problems of monotone operators to nonconvex minimization problems. By assuming generalized concave Kurdyka-Łojasiewicz (KL) property a quadratic regularization objective, we show that FRB converges globally stationary point objective and enjoys finite length property. Convergence rates are also given. The...

an l-fuzzifying matroid is a pair (e, i), where i is a map from2e to l satisfying three axioms. in this paper, the notion of closure operatorsin matroid theory is generalized to an l-fuzzy setting and called l-fuzzifyingclosure operators. it is proved that there exists a one-to-one correspondencebetween l-fuzzifying matroids and their l-fuzzifying closure operators.

We establish the mathematical theory for the steady and unsteady flows of fluids with discontinuous constitutive equations. We consider a model for a fluid that at certain critical value of the shear rate exhibits jumps in the generalized viscosity of a power-law type. Using tools such as Young measures, maximal monotone operators, compact embeddings and energy equality we prove the existence o...