This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving $\mathcal{H}(·,·)$-compression XOR-${\alpha }_{\mathcal{M}}$-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with $\mathcal{H}(·,·)$-compression XOR-${\alpha }_{\mathcal{M}}$-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.

In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.

Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, Boyd–Wong contraction, Pant contraction and relational contraction. We also establish the corresponding uniqueness theorem for the proposed contraction under some additional hypotheses. Several examples are furnished to illustrate the legitimacy of our newly proved results. In particular, we deduce a fixed-point theorem for almost Boyd–Wong contractions in the setting of abstract metric space. Our results generalize, enhance, expand, consolidate and develop a number of known results existing in the literature. The practical relevance of the theoretical findings is demonstrated by applying to study the existence and uniqueness of solution of a specific periodic boundary value problem.

The current article investigates the boundedness criteria for the commutator of rough p -adic fractional Hardy operator on weighted p -adic Lebesgue and Herz-type spaces with the symbol function from weighted p -adic bounded mean oscillations and weighted p -adic Lipschitz spaces.

This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion $\left({\mathrm{S}}_{\mathrm{p}}{\mathrm{VI}}_{\mathrm{s}}\mathrm{P}\right)$ and its extended version for estimating the common solution of $\left({\mathrm{S}}_{\mathrm{p}}{\mathrm{VI}}_{\mathrm{s}}\mathrm{P}\right)$ and fixed point problem $\left(\mathrm{FPP}\right)$ of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example.

This manuscript considers a class of piecewise differential equations (DEs) modeled with the Caputo-Fabrizio differential operator. The proposed problem involves a proportional delay term and is equipped with anti-periodic boundary conditions. The piecewise derivative can be applied to model many complex nature real-world problems that show a multi-step behavior. The existence theory and Hyer-Ulam (HU) stability results are studied for the proposed problem via fixed point techniques such as Banach contraction theorem, Schauder’s fixed point theorem and Arzelá Ascoli theorem. A numerical problem is presented as an example to see the validity and effectiveness of the applied concept.