In this article we introduce the difference double sequence spaces 2`∞(∆, q), 2c(∆, q), 2c0(∆, q), 2c(∆, q), 2c0 (∆, q), 2c (∆, q) and 2c0 (∆, q) defined over a seminormed space (X, q), seminormed by q. We examine some topological and algebraic properties of these spaces like symmetricity, solidness, monotonocity, convergence free, nowhere densenes etc. We prove some inclusion results too.

In this paper, we obtain the existence and the uniqueness of common best proximity point theorems for non-self mappings between two subsets of a complex valued metric space satisfying certain contractive conditions. Our results supported by some examples.

To be written.

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1 Assistant Lecturer; School of Spatial Planning and Natural Resource Management; Jaramogi Oginga Odinga University of Science and Technology, KENYA 2 Seniour Lecturer; School of Spatial Planning and Natural Resource Management; Jaramogi Oginga Odinga University of Science and Technology, KENYA 3 Professor; School of Agriculture and Food Science; Jaramogi Oginga Odinga University of Science and...

The focus of this article is on various approaches to discerning patterns in nonempty sets endowed with a proximity (nearness) relation. Patterns arise in repetitions of some form in the arrangement of the parts of a set. To simplify the steps leading to pattern discovery, an approach inspired by M. Katĕtov is used, where one proximitises certain parts of a nonempty set, rather than proximitise...