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In this paper, we survey iterative algorithms for solving split variational inequalities and fixed point problems in Hilbert spaces. The investigated split problem is involved in two pseudomonotone operators and two pseudocontractive operators. We propose a self-adaptive Tseng-type algorithm for finding a solution of the split problem. Strong convergence of the suggested algorithm is shown under weaker conditions than sequential weak-to-weak continuity imposed on two pseudomonotone operators. [ABSTRACT FROM AUTHOR]

Various azoderivative dyes were incorporated in uncolored poly(vinyl alcohol) (PVOH). One type of film was obtained by drying the layer of solution cast on glass plate. The other type was obtained by rubbing the PVOH layer before complete drying. Linear birefringence and dichroism of dyed polymer films were investigated as a function of stretching degree. An increase in the linear birefringence was found with increasing stretching degree for both uncolored and colored films. Dichroism of the PVOH films depends on the dye chemical structure and also on the stretching degree of both non-rubbed and rubbed and dyed PVOH samples. Molecular modeling was used to examine interactions occurring between PVOH and the embedded dye molecule. These stretching degree dependencies were approximated mathematically, which was used to describe the behavior of some components of interference filters. KEYWORDS blends, dyes/pigments, films, molecular modeling, optics, 1 | INTRODUCTION Dye-containing polymers present both theoretical and practical uses in the development of new products with increased performance. [1] Depending on the properties of the incorporated dye molecules [...]

This paper uses a matriceal technique to study properties of the iterates of Mobius transformations when their coefficients are random variables. The algorithms discussed allow to obtain new fractal structures. [ABSTRACT FROM AUTHOR]

We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the setting and the class of involved operators. More accurately, Hilbert spaces are particular Hadamard spaces, while enriched Suzuki nonexpansive mappings are natural generalizations of enriched nonexpansive mappings. Next, enriched Suzuki nonexpansive mappings naturally contain Suzuki nonexpansive mappings in Hadamard spaces. Besides technical lemmas, the results of this paper deal with (1) the existence of fixed points for enriched Suzuki nonexpansive mappings and (2) Δ and strong (metric) convergence of Picard iterates of the α -averaged mapping, which are exactly Krasnoselskij iterates for the original mapping. [ABSTRACT FROM AUTHOR]

In this work we start from near vector spaces, which we endow with some additional properties that allow convex analysis. The seminormed structure used here will also be improved by adding properties such as the null condition and null equality, thus resulting in a new type of space, which is still weaker than the conventional Banach structures: pre-convex regular near-Banach space. On the newly defined structure, we introduce the concept of uniform convexity and analyze several resulting properties. The major outcomes prove a remarkable resemblance to the classical properties resulting from uniform convexity on hyperbolic metric spaces or modular function spaces, including the famous Browder-Gohde fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X × X × X → X and ɡ : X → X satisfying a nonlinear contraction based on ϕ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results.