(1) If a≤ c and d ≤ b, then [c,d]⊆ [a,b]. (2) If a≤ c and b≤ d and c≤ b, then [a,b]∪ [c,d] = [a,d]. (3) If a≤ c and b≤ d and c≤ b, then [a,b]∩ [c,d] = [c,b]. (4) For every subset A of R1 such that A = [a,b] holds A is closed. (5) If a≤ b, then [a, b]T is a closed subspace of R1. (6) If a≤ c and d ≤ b and c≤ d, then [c, d]T is a closed subspace of [a, b]T. (7) If a≤ c and b≤ d and c≤ b, then [a,...

In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides complete solution to an open problem raised by Zoran D. Mitrovi? (A note on Banach’s space and b-metric space). The result presented the paper generalizes unifies some results theory.

Abstract In this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify corresponding in direction. We consider an example indicate validity obtained results.

For each N ≥ cdn 2d(d+1) d+2 we prove the existence of a spherical ndesign on Sd consisting of N points, where cd is a constant depending only on d.