We establish common fixed point theorems for weakly compatible generalized φcontractions. As applications, various common fixed point and best approximation results for Cq-commuting and compatible maps are derived. Our results unify, extend and complement various known results existing in the literature.

Sergey V. Dmitriev, Avinash Khare, Panayotis G. Kevrekidis, Avadh Saxena and Ljupćo Hadžievski Institute for Metals Superplasticity Problems RAS, 39 Khalturina, Ufa 450001, Russia Institute of Physics, Bhubaneswar, Orissa 751005, India 3 Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA Center for Nonlinear Studies and Theoretical Division, Los A...

* Correspondence: ming@mail. nhcue.edu.tw Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan Full list of author information is available at the end of the article Abstract In this article, we introduce the notions of (j φ)-weak contraction mappings and (ψ φ)-weak contraction mappings in complete generalized metric spaces and prove two theorems which a...

In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...

Several classical facts due to Lyndon, Shenitzer, and Baumslag about ranks of subgroups generated by solutions to equations over the free group are generalized and given a uniform proof. Given a graph of free groups G = Γ(Fi) over cyclic subgroups and a homomorphism φ : G → F which embeds each Fi, there is a natural two complex Xφ which encodes φ. Our strategy for extracting algebraic informati...

In this paper we deal with the following generalized vector quasiequilibrium problem: given a closed convex set K in a normed space X, a subset D in a Hausdorff topological vector space Y , and a closed convex cone C in R. Let Γ : K → 2, Φ : K → 2 be two multifunctions and f : K×D×K → R be a single-valued mapping. Find a point (x̂, ŷ) ∈ K×D such that (x̂, ŷ) ∈ Γ(x̂)× Φ(x̂), and {f(x̂, ŷ, z) : z ∈ Γ(...

Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a non-linear superposition of solutions along the axes x = 0 and y = 0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K = −1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) an...

This paper deals with mainly establishing numerous sets of generalized second-order parametric sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem are achieved based on some partitioning schemes under various types of generalized second-order (F ,β, φ, ρ, θ, m)-univex...

Let A1,A2 be standard operator algebras on complex Banach spaces X1, X2, respectively. For k ≥ 2, let (i1, . . . , im) be a sequence with terms chosen from {1, . . . , k}, and define the generalized Jordan product T1 ◦ · · · ◦ Tk = Ti1 · · ·Tim + Tim · · ·Ti1 on elements in Ai. This includes the usual Jordan product A1 ◦ A2 = A1A2 + A2A1, and the triple {A1, A2, A3} = A1A2A3 + A3A2A1. Assume th...

Let P(G;x,y) be the number of vertex colorings φ : V →{1, ...,x} of an undirected graph G = (V,E) such that for all edges {u,v} ∈ E the relations φ(u)≤ y and φ(v)≤ y imply φ(u) 6= φ(v). We show that P(G;x,y) is a polynomial in x and y which is closely related to Stanley’s chromatic symmetric function, and which simultaneously generalizes the chromatic polynomial, the independence polynomial, an...