Lemma 3 On a well-ordered set, a strictly monotone function is extensive. Proof. Assume that S = {x ∈ X | x > f(x)} 6= ∅. Then, let a be the least element of S (X is well ordered). Hence, a > f(a). By strict monotony, f(a) > f(f(a)). Therefore, f(a) ∈ S and a ≤ f(a). Contradiction. Lemma 4 If f is a monotone injection from α to β, then α ≤ β. Proof. Since α is well ordered, f is extensive. Henc...

In this study, we introduce a new notion, so-called KW-type F-contraction mapping, inspired by the ideas of Wardowski and Klim–Wardowski. Then, investigate existence best proximity point for such mappings considering family, which is larger than family functions that often used in fixed-point results multivalued mappings. To demonstrate effectiveness our result, also give comparative example to...

‎In this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎We show that if F is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎Rad(F)=F‎. ‎We proved the extension theorem for radical of filters in residuated lattices‎. ‎Also‎, ‎we study the radical‎ ‎of filters in linearly o...

The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.

We prove a common fixed points of four mappings satisfying a contraction type in partially ordered metric spaces. Mathematics Subject Classification: 47H10, 54H25

Motivated by the ideas of F -weak contractions and id="M3"> , R g -contractions, notion id="M4"> w -contractions is introduced studied in present paper. The idea to establish some interesting res...

For a family of graphs F , the F-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists S ⊆ E(G) of size at most k such that G/S belongs to F . Here, G/S is the graph obtained from G by contracting all the edges in S. Heggernes et al. [Algorithmica (2014)] were the first to study edge contraction problems in the realm of Parameterized Complex...