16 Results Found

This paper deals with the study of mixed variational-like inclusions involving Yosida approximation operator (MVLIYAO) and η-proximal mapping in Banach spaces. It is investigated that (MVLIYAO) is equivalent to fixed point problems in Banach spac...

We focus our study on a co-variational inequality problem involving two generalized Yosida approximation operators in real uniformly smooth Banach space. We show some characteristics of a generalized Yosida approximation operator, which are used in o...

In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that ou...

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type mu...

Given an injective closed linear operator A defined in a Banach space $X,$ and writing ${}_{CF}{D}_t^{\alpha }$ the Caputo–Fabrizio fractional derivative of order $\alpha \in (0,1),$ we show that the unique solution of the abstract Cauchy problem $(\ast ){}_{CF}$...

In this paper, we address a variational problem involving the sum of two maximal monotone operators combined with a finite family of nonexpansive operators. To solve this problem, we propose iterative algorithms based on single-valued mappings. First...

This article studies the structure and properties of real-ordered Hilbert spaces, highlighting the roles of the XOR and XNOR logical operators in conjunction with the Yosida and Cayley approximation operators. These fundamental elements are utilized...

A new generalized Yosida inclusion problem, involving $\mathcal{A}$-relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence res...

In this paper, we study a variational inclusion problem in a real ordered Hilbert space via an averaged-operator-based approach. The proposed framework combines Yosida and Cayley approximation operators with the logical XOR and XNOR operations, resul...

In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz c...

In this paper, we study an absolutely new problem, namely, the Cayley inclusion problem which involves the Cayley operator and a multi-valued mapping with XOR-operation. We have shown that the Cayley operator is a single-valued comparison and it is L...

It is a well-known fact that the Dzhrbashyan–Nersesyan fractional derivative includes as particular cases the fractional derivatives of Riemann–Liouville, Gerasimov–Caputo, and Hilfer. The notion of resolving a family of operators f...

In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists an...

The system of extended ordered XOR-inclusion problems (in short, SEOXORIP) involving generalized Cayley and Yosida operators is introduced and studied in this paper. The solution is obtained in a real ordered Banach space using a fixed-point approach...

In this paper, we consider a 2D stochastic quasi-geostrophic equation driven by jump noise in a smooth bounded domain. We prove the local existence and uniqueness of mild $L^p(D)$-solutions for the dissipative quasi-geostrophic equation with a full...

This article establishes a strong averaging principle for a class of slow-fast stochastic evolution systems that incorporate both McKean–Vlasov interactions and multivalued operators within a Hilbert-space variational framework. The slow variab...