B-Convexity, B-1-Convexity, and Their Comparison

A subset U of R-+(n) is B-convex if for all x, y is an element of U and all lambda is an element of [0, 1] one has lambda x proves y is an element of U. These sets were introduced and studied by Briec, Horvath, Rubinov and Adilov [7, 8, 10]. A subset V of is B-1-convex if for all x, y is an element of V and all lambda is an element of [1, infinity) one has lambda x perpendicular to y is an element of V. This concept is defined and studied by Adilov, Briec, and Yesilce. In this work, B-convex and B-1-convex functions are defined and some fundamental theorems about these functions are proved, additionally some important properties of B-convex and B-1-convex sets are compared then the construction of sets is described with graphics.