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In the present paper, we study linear operators $$\Delta $$ from the algebra of $$2\times 2$$ matrices $${\mathbb {M}}_2({\mathbb {C}})$$ into its tensor square. Each such kind of mapping defines a quadratic operator on the state space of $${\mathbb {M}}_2({\mathbb {C}})$$ . We know that q-purity of quasi quantum quadratic operators (q.q.o.) is equivalent to the invariance of the unite sphere under the corresponding quadratic operator. Therefore, in the paper, we consider quadratic operators, which preserve the unit circle, and show that the corresponding quasi q.q.o. cannot be not positive. Note that this is a much weaker condition than the q-purity of quasi q.q.o. Moreover, we will classify q-pure circle preserving quadratic operators into three disjoint classes (non isomorphic). Moreover, we are able to show that quasi q.q.o. corresponding to the first class is block positive. Note that the block positivity is weaker than positivity. This kind of operator, i.e., not positive but block-positive operator allows us to detect that the given state on $${\mathbb {M}}_2({\mathbb {C}})\otimes {\mathbb {M}}_2({\mathbb {C}})$$ is either entangled or not. The obtained results will allow us to verify whether a given mapping is positive or not. This finding suggests us to produce a class of non-positive mappings. Moreover, it will shed some light in finding entanglement states. [ABSTRACT FROM AUTHOR]

The paper proposes an explicit parallel iterative algorithm for solving variational inequalities over the intersection of fixed point sets of finitely many demicontractive mappings. The algorithm combines the steepest descent method with the Krasnosel'skii-Mann type method and the splitting-up technique. The strongly convergent theorem is established under fewer restrictions imposed on parameters and mappings. Several applications of the algorithm to other problems are presented. We also illustrate the convergence of the algorithm and compare it with others by considering some preliminary numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider a differential inclusion governed by a set-valued nonexpansive mapping and study the asymptotic behavior (weak and strong convergence) of its solutions with various assumptions on this mapping. Then for a set-valued nonexpansive mapping, we define the corresponding resolvent (proximal) operator as a set-valued mapping and study some of its elementary properties. Subsequently, we apply the resolvent operator to state the implicit discretization of the differential inclusion and study the asymptotic behavior of its solutions which yields similar convergence results as in the continuous case. This provides an algorithm for approximating a fixed point of a set-valued nonexpansive mapping which extends the classical proximal point algorithm. An application to variational inequalities and a numerical comparison with another iterative method for approximating a fixed point of set-valued nonexpansive mappings are also presented. [ABSTRACT FROM AUTHOR]

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate some fixed-point theorems in modular metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a new class of nonlocal boundary value problems of fractional differential equations and inclusions with a new integral boundary condition. This new boundary condition states that the value of the unknown function at an arbitrary (local) point $$\xi $$ is proportional to the contribution due to a sub-strip of arbitrary length $$(1-\eta ),$$ that is, $$x(\xi )=a \int _{\eta }^{1}x(s)\mathrm{d}s,$$ where $$0< \xi < \eta <1$$ and a is constant of proportionality. The existence of solutions for the given problems is shown by means of contraction mapping principle, a fixed point theorem due to O'Regan and nonlinear alternative for multivalued maps. The results are well illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce graphic contraction mappings in b-metric spaces and establish some fixed point theorems in the aforesaid space. Appropriate graphs are presented to visualize related definitions and concepts. On the other hand, some examples are presented to verify the authenticity and effectiveness of the established results. Our results generalize and extend some pioneer results existing in the literature. Moreover, applications to existence of solution for ordinary differential equations and for integral equations are also established to show the adequacy of our results. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a family of univalent harmonic mappings, which map the unit disk onto domains convex in the direction of the imaginary axis. We find conditions for the linear combinations of mappings from this family to be univalent and convex in the direction of the imaginary axis. Linear combinations of functions from this family and harmonic mappings obtained by shearing of analytic vertical strip mappings are also studied. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain several sharp inequalities of homogeneous expansion for the subclass of all normalized almost starlike mappings of order α defined on the unit ball B of a complex Banach space X. Then, with these sharp inequalities, we derive the sharp estimates of the third and fourth homogeneous expansions for the above mappings defined on the unit polydisk Dn in Cn. [ABSTRACT FROM AUTHOR]

In this paper, we study convergence of modified Ishikawa iteration process involving a pair of hybrid mappings satisfying a generalized nonexpansive condition on Banach spaces. In process, several relevant results are generalized and improved. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new fixed point theorems for a 2×2 block operator matrix defined on nonempty, bounded, closed, and convex subsets of Banach algebras, where the inputs are multi-valued mappings. The obtained results are then applied to a coupled system of perturbed functional differential inclusions of initial and boundary value problems in order to prove the existence of solutions under a Carathéodory condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider of finding efficient solution and weakly efficient solution for nonconvex vector optimization problems. When X and Y are normed spaces, F is an anti-Lipschitz mapping from X to Y, and the ordering cone is regular, we present an algorithm to guarantee that the generated sequence converges to an efficient solution with respect to normed topology. If the domain of the mapping is compact, we prove that the generated sequence converges to an efficient solution with respect to normed topology without requiring that mapping is anti-Lipschitz. We also give an algorithm to guarantee that the generated sequence converges to a weakly efficient solution with respect to normed topology. [ABSTRACT FROM AUTHOR]

In this paper, first, a sufficient condition for almost convex mappings of order $$\alpha $$ defined on the unit ball of complex Hilbert spaces and another sufficient condition for almost quasi-convex mappings of order $$\alpha $$ defined on the unit ball of complex Banach spaces are given. Second, the distortion theorem of the Fréchet derivative for almost convex mappings of order $$\alpha $$ on the unit ball of complex Banach spaces, the homogeneous ball of complex Banach spaces, and the unit ball of complex Hilbert spaces are established respectively. Finally, the distortion theorem of the Jacobi determinant for almost convex mappings of order $$\alpha $$ on the Euclidean unit ball in $$\mathbb {C}^n$$ is obtained. Our results generalize many known results. [ABSTRACT FROM AUTHOR]

In this paper, we study the solvability of a system of vector equilibrium problems. We extend the concept of topological pseudomonotonicity to a family of mappings. We prove existence results for the system of vector equilibrium problems under topological pseudomonotonicity conditions by the Kakutani-Fan-Glicksberg fixed point theorem. As applications, we obtain existence results for systems of equilibrium problems under topological pseudomonotonicity conditions. [ABSTRACT FROM AUTHOR]

Let $${\mathcal S}$$ denote the set of all univalent analytic functions $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n$$ on the unit disk $$\mathbb {D}$$ . In 1946, B. Friedman found that the set $$\mathcal S$$ of those functions which have integer coefficients consists of only nine functions. In 1985, authors determine all functions in $${\mathcal S}$$ whose coefficients are integers in complex quadratic fields. The first aim of this paper is to determine the class of univalent sense-preserving harmonic mappings $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n+\sum _{n=1}^{\infty }\overline{b_n} \overline{z^n}$$ with the coefficients $$a_n$$ , $$b_n$$ , $$n=2, 3, \cdots $$ , in a fixed complex quadratic field $$Q(\sqrt{d}i)$$ , where d is a positive square-free integer. Then, under the condition F is sense-preserving in $$\mathbb {D}$$ and $$h'(z)\ne 0$$ or F is sense-reversing in $$\mathbb {D}$$ and $$g(z)\equiv 0$$ , we determine all univalent biharmonic mappings $$F(z)=|z|^2(h(z)+\overline{g(z)})=|z|^2(z+\sum _{n=2}^{\infty }a_n z^n+\sum _{n=1}^{\infty }\overline{b_n} \overline{z^n})$$ , where $$a_n, b_n\in Q(\sqrt{d}i)$$ , $$n=2, 3, \cdots $$ . [ABSTRACT FROM AUTHOR]

In this paper, we present a modular version of KKM and generalized KKM mappings and then we establish a characterization of generalized KKM mappings in modular spaces. Also we prove an analogue to KKM principle in modular spaces. Moreover, as an application, we give some sufficient conditions which guarantee existence of solutions of minimax problems in which we get Fan's minimax inequality in modular spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. Using the contraction mapping principle, Krasnosel'skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are provided for illustrating the applications of our theoretical analysis. [ABSTRACT FROM AUTHOR]

Following Clunie and Sheil-Small, the class of normalized univalent harmonic mappings in the unit disk is denoted by $${\mathcal {S}}_{{\mathcal {H}}}$$ . The aim of the paper is to study the properties of a subclass of $${\mathcal {S}}_{{\mathcal {H}}}$$ , such that the analytic part is a convex function. We establish estimates of some functionals and bounds of the Bloch's constant for co-analytic part. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a concept of graph convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping in Banach spaces and prove an equivalence theorem between graph convergence and resolvent operator convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping. Further, we consider a system of generalized variational inclusions involving $$H(\cdot ,\cdot )$$ -co-accretive mapping in real $$q$$ -uniformly smooth Banach spaces. Using resolvent operator technique, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions under some suitable conditions. Further, we discuss the convergence of iterative algorithm using the concept of graph convergence. Our results can be viewed as a refinement and generalization of some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a $$\varphi $$ -weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we first give some properties for generalized hybrid mappings in complete CAT(0) spaces. Then we prove $$\Delta $$ -convergence and strong convergence theorems of the proposed Picard, Mann, and Ishikawa iterative schemes for such mappings in complete CAT(0) spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend some results of Feng and Liu , Klim and Wardowski , Ćirić and others from the context of metric spaces to cone metric spaces using the concept of sequentially lower semicontinuous. Examples are provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

In 2002 Markov interval maps were introduced by S. Holte. It was shown that any two inverse limits with Markov interval bonding maps with the same pattern were homeomorphic. In this article we introduce generalized Markov interval functions, which are a generalization of Markov interval maps to set-valued functions, and show that any two generalized inverse limits with generalized Markov interval bonding functions with the same pattern are homeomorphic. [ABSTRACT FROM AUTHOR]

Let R be a unital prime ∗-ring containing a nontrivial symmetric idempotent. For A,B∈R, the skew commutator and 2-skew commutator are defined, respectively, by ∗[A,B]=AB-BA∗ and ∗[A,B]2=∗[A,∗[A,B]]. Let Φ:R→R be a surjective map. We show that (1) Φ satisfies ∗[Φ(A),Φ(B)]=∗[A,B] for all A,B∈R if and only if there exists λ∈{-1,1} such that Φ(A)=λA for all A∈R; (2) Φ satisfies ∗[Φ(A),Φ(B)]2=∗[A,B]2 for all A,B∈R if and only if there exists λ∈CS with λ3=I such that Φ(A)=λA for all A∈R, where I is the unit of R and CS is the symmetric extend centroid of R. This is then applied to prime C∗-algebras, factor von Neumann algebras and indefinite self-adjoint standard operator algebras to get a complete invariant for the identity map and to symmetric standard operator algebras as well as matrix algebras. [ABSTRACT FROM AUTHOR]

The purpose of this article is twofold. The first is to prove algebraical dependence of meromorphic mappings from Cm into Pn(C) sharing few moving hyperplanes. The second is to show uniqueness theorem for meromorphic mappings from the viewpoint of dependence. These results improve and extend some earlier works. [ABSTRACT FROM AUTHOR]

We introduce a special kind of almost geodesic mappings of the first type $$\pi _1^*$$ of spaces with non-symmetric affine connections. Also, we investigate a special class of equitorsion almost geodesic mappings of type $$\pi _1^*$$ and find some invariant geometric objects of these mappings. [ABSTRACT FROM AUTHOR]

Recent investigations into what geometric properties are preserved under the convolution of two planar harmonic mappings on the open unit disk $${\mathbb {D}}$$ have typically involved half-plane and strip mappings. These results rely on having a convolution that is locally univalent and sense-preserving on $${\mathbb {D}}$$ , and thus, much focus has been on trying to satisfy this condition. We introduce a family of right half-strip harmonic mappings, $$\Psi _c : {\mathbb {D}}\rightarrow {\mathbb {C}}$$ , $$c>0$$ , and consider the convolution $$\Psi _c * f$$ for a harmonic mapping $$f = h +\overline{g}: {\mathbb {D}}\rightarrow {\mathbb {C}}$$ . We prove it is sufficient for $$h \pm g$$ to be starlike for $$\Psi _c *f$$ to be locally univalent and sense-preserving. Moreover, $$\Psi _c * f$$ decomposes into a convex combination of two harmonic mappings, one of which is f itself. This decomposition is key in addressing mapping properties of the convolution, and from it, we produce a family of convex octagonal harmonic mappings as well some other families of convex harmonic mappings. Additionally, motivated by the construction of $$\Psi _c$$ , we introduce a generalized harmonic Bernardi integral operator. We demonstrate convolution preserving properties and a weak subordination relationship for this extended operator. [ABSTRACT FROM AUTHOR]

We consider the problem of describing the form of biderivations of a triangular ring. Our approach is based on the notion of the maximal left ring of quotients, which enables us to generalize Benkovič's result on biderivations (Benkovič in Linear Algebra Appl 431:1587-1602, 2009). Our result is applied to block upper triangular matrix rings and nest algebras. [ABSTRACT FROM AUTHOR]

We establish exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the generalized Riccati equation, we derive exact solutions to this model for two different wave speed. [ABSTRACT FROM AUTHOR]

We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous generalized asymptotically nonexpansive mappings in Hilbert spaces. As a consequence, results on convergence to a common fixed point of a finite family of uniformly continuous asymptotically nonexpansive in the intermediate sense and asymptotically nonexpansive mappings are proved. [ABSTRACT FROM AUTHOR]

Let $$\mathcal {A}$$ be a unital Banach algebra and $$\mathcal {M}$$ be a unital Banach $$\mathcal {A}$$ -bimodule. The main results characterize a continuous linear map $$\varphi :\mathcal {A}\rightarrow \mathcal {M}$$ that satisfies $$a\varphi (a^{-1})=\varphi (1)$$ or $$a\varphi (a^{-1})+ \varphi (a^{-1}) a=2\varphi (1)$$ for all $$a$$ in principal component of invertible elements of $$\mathcal {A}$$ . The proof is based on the consideration of a continuous bilinear map satisfying a related condition. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new class of non-self mappings, called weak proximal contractions, which contains the proximal contractions as a subclass. Existence and uniqueness results of a best proximity point for weak proximal contractions are obtained. Also, we provide sufficient conditions for the existence of common best proximity points for two non-self mappings in metric spaces having appropriate geometric property. Examples are given to support our main results. [ABSTRACT FROM AUTHOR]