(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,...

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.

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...

In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.

an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

the study of stability problems of functional equations was motivated by a question of s.m. ulam asked in 1940. the first result giving answer to this question is due to d.h. hyers. subsequently, his result was extended and generalized in several ways.we prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=ag(x)+bg(y)on restricted domain. namely, we show, under some weak natural...

‎in this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{t}^{kappa^{2}}}:=j,;;1

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this article is devoted to the study of existence and multiplicity of positive solutions to aclass of nonlinear fractional order multi-point boundary value problems of the type−dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where dq0+ represents standard riemann-liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞...