Endpoint results are presented for multi-valued cyclic contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Nadler (1969), Daffer-Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inco...

Several classical facts due to Lyndon, Shenitzer, and Baumslag about ranks of subgroups generated by solutions to equations over the free group are generalized and given a uniform proof. Given a graph of free groups G = Γ(Fi) over cyclic subgroups and a homomorphism φ : G → F which embeds each Fi, there is a natural two complex Xφ which encodes φ. Our strategy for extracting algebraic informati...

We introduce and compute the class of a number of effective divisors on the moduli space of stable maps M0,0(P,d), which, for small d, provide a good understanding of the extremal rays and the stable base locus decomposition for the effective cone. We also discuss various birational models that arise in Mori’s program, including the Hilbert scheme, the Chow variety, the space of k-stable maps, ...

The notion of generalized Berinde type contraction non-self maps in partially ordered metric spaces is introduced, and some best proximity point theorems for this class are established. Mathematics Subject Classification: 47H10, 54H25

UNLABELLED PURPOSETo review the topographic patterns associated with keratoconus suspects and provide criteria for keratoconus screening. METHODS Case study using maps from the NIDEK OPD-Scan II and OPD Station to highlight patterns seen in keratoconic corneas. RESULTS Five criteria are listed for the detection of keratoconus: 1) apex of the cone is not centered at the 6-o'clock semi-meridi...

in this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. meantime, an example is provided toillustrate this theorem. the main result shows that a self-mappingon a g-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. afterwards, some results inco...

Robinson’s generalized Newton’s method for nonlinear functions with values in a cone is extended to mappings on Riemannian manifolds with values in a cone. When Df satisfies the L-average Lipschitz condition, we use the majorizing function technique to establish the semi-local quadratic convergence of the sequences generated by the extended Newton’s method. As applications, we also obtain Kanto...

The notion of generalized almost Geraghty type contraction non-self maps in partially ordered metric spaces is introduced, and some new best proximity point theorems for this class are established. Mathematics Subject Classification: 47H10, 54H25

The paper is devoted to the study of general nonsmooth problems of cone-constrained optimization (or conic programming) important for various aspects of optimization theory and applications. Based on advanced constructions and techniques of variational analysis and generalized differentiation, we derive new necessary optimality conditions (in both " exact " and " fuzzy " forms) for nonsmooth co...