Given two maps f1, f2 : M −→ N between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC(f1, f2) of pathcomponents of the coincidence space of maps f ′ 1 , f ′ 2 where f ′ i is homotopic to fi, i = 1, 2 ? Approaching this question via normal bordism theory we define a lower bound N(f1, f2) which gener...

In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments    D 0+u(t) + a(t)f(u(θ(t))) = 0, 0 < t < 1, n− 1 < α ≤ n, u(i)(0) = 0, i = 0, 1, 2, · · · , n− 2, [D 0+ u(t)]t=1 = 0, 1 ≤ β ≤ n− 2, where n > 3 (n ∈ N), D 0+ is the standard Riemann-Liouville fractional derivative of order α, f : [0,∞) → [0,∞), a : [0, 1] → (0,∞) and θ : (0, ...

Abstract The purpose of this paper is to present the notion MR-Kannan type contractions using generalized averaged operator. Several examples are provided illustrate concept presented herein. We provide a characterisation normed spaces with fixed point. investigate Ulam–Hyers stability and well-posedness result for mappings here.

The Lefschetz fixed point theorem follows easily from the identification of the Lefschetz number with the fixed point index. This identification is a consequence of the functoriality of the trace in symmetric monoidal categories. There are refinements of the Lefschetz number and the fixed point index that give a converse to the Lefschetz fixed point theorem. An important part of this theorem is...