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In this paper, we study several classes of split inverse problems. We start with the split common fixed point problem with multiple output sets for multivalued demicontractive mappings. A relaxed inertial iterative method for solving this problem is presented and analysed. Furthermore, the method is applied to a system of split variational inequalities, system of split equilibrium problem and other related split problems. Several numerical experiments illustrate and validate the applicability of our proposed method. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate a generalized differential mixed quasi-variational inequality consisting of a system of an ordinary differential equation and a generalized mixed quasi-variational inequality. By using an important result concerning the measurable selection, we prove the existence of Carath'eodory weak solution to the generalized differential mixed quasi-variational inequality. Then, with the existence result, we establish two stability results for the generalized differential mixed quasi-variational inequality under different conditions, i.e., upper semicontinuity and lower semicontinuity of the Carath'eodory weak solution with respect to the parameter, which is a perturbation of some mappings in the generalized mixed quasi-variational inequality. [ABSTRACT FROM AUTHOR]

In this paper, we begin by discussion of some well known results on the existence of left invariant means in the spaces: LUC(S);AP(S) andWAP(S) with Hahn-Banach extension theorem. We then give a new and precise proof of the well known Fan-Glicksberg fixed point theorem. This is then followed by a discussion on some related open problems. [ABSTRACT FROM AUTHOR]

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce a class of generalized contractions in the sense of Berinde. Some examples and fixed point theorems for such introduced mappings in the setting of metric spaces endowed with a graph are discussed. Our results extend and include many existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a semi-cyclic Berinde contraction pair on a metric space which is more general than that of semi-cyclic contraction pair defined by Gabeleh and Abkar [Gabeleh, M. and Abkar, A., Best proximity points for semi-cyclic contractive pairs in Banach spaces, Int. Math. Forum, 6 (2011), 2179-2186] and prove an existence result concerning global monomization of best proximity points of this pair. Our main result can be used to obtain a common fixed point theorem of some contractive mappings related to Berinde's contractions without commutative assumption. An example supporting our main result is also given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37-53]. [ABSTRACT FROM AUTHOR]

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536-545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for non-self G-almost contractive mappings in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein. [ABSTRACT FROM AUTHOR]

In this paper, we give examples of cyclic operators defined on various types of sets, in order to illustrate some results in the extremely rich literature following the seminal paper [Kirk,W. A., Srinivasan, P. S. and Veeramani, P., Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), No. 1, 79 - 89]. All examples which are presented enrich the list of cyclic operators and give a subject to future studies of this type of operators. [ABSTRACT FROM AUTHOR]

Let E be a real normed linear space. A subset X ⊂ E is called a retract of E if there exists a continuous mapping r : E → X, a retraction, satisfying r(x) = x, x ⊂ X. It is well known that every nonempty closed convex subset of E is a retract of E. Nonconvex retracts are studied in this paper. [ABSTRACT FROM AUTHOR]

The concept of stratified graph introduces some method of knowledge representation (see [Ţăndăreanu, N., Knowledge representation by labeled stratified graphs, Proc. 8th World Multi-Conference on Systemics, Cybernetics and Informatics, 5 (2004), 345-350; Ţăndăreanu, N., Proving the Existence of Labelled Stratified Graphs, An. Univ. Craiova Ser. Mat. Inform., 27 (2000), 81-92]) The inference process developed for this method uses the paths of the stratified graphs, an order between the elementary arcs of a path and some results of universal algebras. The order is defined by considering a structured path instead of a regular path. In this paper we define the concept of system of knowledge representation as a tuple of the following components: a stratified graph G, a partial algebra Y of real objects, an embedding mapping (an injective mapping that embeds the nodes of G into objects of Y ) and a set of algorithms such that each of them can combine two objects of Y to get some other object of Y. We define also the concept of inference process performed by a system of knowledge processing in which the interpretation of the symbolic elements is defined by means of natural language constructions. In this manner we obtained a mechanism for texts generation in a natural language (for this approach, Romanian). [ABSTRACT FROM AUTHOR]

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (κ) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we study a zero point problem of the sum of two accretive operators based on a viscosity forward-backward iterative algorithm with computational errors. Strong convergence results are established in the framework of q-uniformly smooth Banach spaces. We also apply the strong convergence results to solve variational inequality problems, convex minimization problems and fixed point problems. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iterative process involving a hybrid pair of a Bregman strongly nonexpansive single-valued mapping and a finite family of Bregman relative nonexpansive multi-valued mappings and prove strong convergence theorems of the proposed iterative process in reflexive Banach spaces under appropriate conditions. Our main results can be viewed as an improvement and extension of the several results in the literature. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce a class of generalized contractions in product spaces in the sense of Prešić. Some examples and fixed point theorems for such introduced mappings in the setting of orbitally complete metric spaces are proved. The results presented here extend and include many existing several results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators, for which a fixed point theorem is proven. This class of mappings is very large and unifies several classes of contractive type operators from the literature, including Berinde mappings. Such fact is proven via a comparison with various metrical contractive type mappings. [ABSTRACT FROM AUTHOR]

We prove that a cyclic coordinate fixed point algorithm for nonexpansive mappings when the underlying Hilbert space is decomposed into a Cartesian product of finitely many block spaces is weakly convergent to a fixed point of the mapping under investigation. Our result relaxes a condition imposed on the stepsizes of Theorem 3.4 of Chow, et al [Chow, Y. T., Wu, T. and Yin, W., Cyclic coordinate-update algorithms for fixed-point problems: analysis and applcations, SIAM J. Sci. Comput., 39 (2017), No. 4, A1280-A1300]. [ABSTRACT FROM AUTHOR]

The split common fixed points problem for demicontractive operators has been studied in Hilbert spaces. An iterative algorithm is considered and the weak convergence result is given under some mild assumptions. [ABSTRACT FROM AUTHOR]

We improve a recent accelerated proximal gradient (APG) method in [Li, Q., Zhou, Y., Liang, Y. and Varshney, P. K., Convergence analysis of proximal gradient with momentum for nonconvex optimization, in Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, PMLR 70, 2017] for nonconvex optimization by allowing variable stepsizes. We prove the convergence of the APG method for a composite nonconvex optimization problem under the assumption that the composite objective function satisfies the Kurdyka-Łojasiewicz property. [ABSTRACT FROM AUTHOR]

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1-14], we introduce a new class of G-f-contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph. [ABSTRACT FROM AUTHOR]

We study monotone nonexpansive self-mappings of a closed and convex cone in an ordered Banach space with particular emphasis on the asymptotic behavior of their inexact iterates. [ABSTRACT FROM AUTHOR]

We improve Bogin-type fixed point theorems in complete metric spaces. We also compare these theorems with a Ćirić-type fixed point theorem and others. [ABSTRACT FROM AUTHOR]

The purpose of this work is to present some existence results for common fixed point theorems for Geraghty contraction mappings with two generalized metrics endowed with a directed graph in JS-metric spaces. Some examples supported our main results are also presented. [ABSTRACT FROM AUTHOR]