. In this paper, we extends the classical theory of variational inequalities to the hyperbolic scalar setting using the structure of D-Hilbert spaces. We introduce and analyze a new class of variational inequalities, termed general mildly D-nonlinear variational inequalities, which generalize classical formulations by incorporating Dnonlinear and product-type mappings. We characterize these problems in terms of their idempotent components and demonstrate that several known variational inequality problems, including Stampacchia-type and complementarity problems, emerge as special cases.
. Let 7-t be a complex Hilbert space of dimension at least 3, and let B(H) denote the algebra of all bounded linear operators on H. Based on results by Molnar, this paper revisits the problem addressed in [18], which characterizes surjective maps Phi: B(H) - B(H) that preserve the set of partial isometric operators in both directions. We focus exclusively on the linear case, rather than the more general additive case. Furthermore, we provide an alternative proof of the main result in [9] from a different point of view. Finally, we propose new directions for exploring maps that preserve higher-order partial isometric operators in both directions.
We show the existence of solutions satisfying Cauchy or terminal boundary conditions for first order differential inclusion (phi(x(t)))' is an element of F(t, x(t)). We consider the second order problem (phi(x'(t)))' is an element of F(t, x(t)) with many boundary conditions. The set-valued map F has non-convex values and the function phi satisfies a weak condition. The resolution method use the topological degree without the method of upper and lower solutions.
(tau(1),tau(2))-star-Lindelo & uml;fness ensures that for every pair (U-1 subset of tau(1), U-2 subset of tau(2)) of open covers, a countable subcover of U-1, can spread through U-2 via the star operation to cover the entire bitopological space (X, tau(1), tau(2)). Giving a positive answers to the questions of Choudhury et. al. [12], DCCC and meta-Lindelo & uml;f like characterization of star-Lindelo & uml;f bitopological spaces are presented in this paper. It has been established that a JDCCC bitopological space is both (tau(1), tau(2))-2-star-Lindelo & uml;f and ( tau(2), tau(1))-2-star-Lindelo & uml;f. And if a bitopological space which is both (tau(1),tau(2))-n-star-Lindelo & uml;f (n is an element of N) and ( tau(1), tau(2))-meta-Lindelo & uml;f, then (X, tau(2)) is (n-1)-star Lindelo & uml;f (0-star-Lindelo & uml;fness represents Lindelo & uml;fness).
In this paper, a new class of H-monotone in Banach spaces is considered and studied. The resolvent operator and Cayley approximation operator associated with the H-monotone are defined, and the Lipschitz continuity of Cayley approximation operator is also established. An application involves the solvability of a class of generalized Cayley inclusions with H-monotone in Banach spaces. By utilizing the technique of resolvent, an iterative algorithm is developed for solving such a class of generalized Cayley inclusions in Banach spaces. The convergence of the iterative sequence generated by the algorithm is proven under certain suitable conditions. The results are justified by means of a numerical example analytically and graphically using Python(matplotlib).
In this paper, we study uniform ergodicity for C-0-semigroups of universally bounded operators acting on locally convex spaces. Characterizations of uniform ergodic C-0-semigroups are given. Importantly, we give a C-0-semigroups version of F. Pater, T. Binzar [14] theorem.
In this paper, we introduce generalized multivalued F-proximal contraction mappings within the partial metric spaces framework and establish best proximity point results for such mappings. The best proximity point theorem for multivalued F-proximal contraction mappings involving alpha-admissibility is also obtained. Several related results in the literature are unified and generalized by our new best proximity point results. We also provide nontrivial examples to support our findings. Finally, we derive an existence of a solution to an integral equation that validates our finding.
This paper introduces and investigates the class of k-quasi -power posinormal operators} in Hilbert spaces, generalizing both posinormal and -power posinormal operators. We establish fundamental properties including matrix representations in block 2x2 form, tensor product preservation (T circle times S remains in the class when T,S are), and complete characterizations for weighted conditional type operators T-wu := wE(uf) on L-2 Sigma. Key theoretical contributions include a structural decomposition theorem for operators with non-dense range, spectral properties, invariant subspace behavior, and interactions with isometric operators. For weighted operators, we derive explicit conditions for k-quasi n-power posinormality in terms of weight functions w,u and their conditional expectations. The work bridges abstract operator theory with concrete applications, particularly in conditional expectation analysis, while significantly extending posinormal operator theory. The results provide new tools for operator analysis with potential applications in spectral theory, functional calculus, and mathematical physics. Concrete examples throughout the paper illustrate the theory, and the framework opens new research directions in operator theory and its applications, offering both theoretical insights and practical computational tools for analyzing this important class of operators in Hilbert spaces
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics and its applications, including operator theory, functional analysis, and quantum mechanics. Understanding their spectral behavior is essential for analyzing the dynamics and stability of systems governed by such operators. P-matrix is one of the important types of matrices appearing in linear complementarity problems. In this research, with the help of spectral results we have given a factorization for P-matrix, as the product of two non-trivial P-matrices. We also focus on elucidating spectral properties such as eigenvalues, approximate eigenvalues and spectral values associated with certain positive operators.
In this paper, we introduce a new class of contractive mappings, called generalized Psi -Geraghty contractions, in the framework of b-complete metric spaces. We establish a unique fixed-point theorem that extends existing results in fixed-point theory. An illustrative example with a graphical representation demonstrates the validity of our findings. Furthermore, we apply the main result to an integral equation, highlighting its effectiveness in ensuring the existence and uniqueness of solutions. This work underscores the theoretical significance and practical applicability of generalized Psi -Geraghty contractions in mathematics, physics, and engineering.
. The primary objective of this paper is to present and investigate an inertial Krasnoselski-Mann (KM) type iterative method for approximating a common solution to a split monotone variational inclusion problem and a hierarchical fixed point problem for a finite family of l-strictly pseudocontractive non-self mappings. Additionally, we demonstrate that the iterative sequences provided by the proposed method converge weakly to a common solution to these problems. The methodology and conclusions described in this work extend and unify previously published findings in this domain. Finally, a numerical example is presented to demonstrate the suggested iterative method's convergence analysis of the sequences obtained. We also carried out a justification how the inertial term is useful.
