We find the universal module w(M) for functions (that need not be invariants) of finite matroids, defined on a minor-closed class M and with values in any module L over any commutative and unitary ring, that satisfy a parametrized deletion-contraction identity, F (M) = δeF (M r e) + γeF (M/e), when e is neither a loop nor a coloop. (F is called a (parametrized) weak Tutte function.) Within the ...

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems −div(φ(|∇u|)∇u)− b(u)u ∈ λ∂F (x, u) in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded domain, N ≥ 2 and ∂F (x, u) is a generalized gradient of F (x, t) with respect to t. The main tools utilized are Variational Methods for Locally Lipschitz Functional and a Concentration Compactness T...

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

The well-known Banach’s fixed point theorem asserts that if D = X, f is contractive and (X, d) is complete, then f has a unique fixed point in X. In nonlinear analysis, the study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been investigated deeply. The Banach contraction principle [1] is one of the initial and crucial results in thi...

The theory of iterated function systems (IFSs) has been an active area research on fractals and various types self-similarity in nature. basic theoretical work IFSs proposed by Hutchinson. In this paper, we introduce a new generalization Hutchinson IFS, namely generalized ?-contraction which is finite collection functions T1,…,TN from Cartesian product space X×?×X into X, where (X,d) complete m...

In this paper, we study to approximate fixed points of Suzuki generalized multivalued nonexpansive mappings by using a three-step iterative scheme (1.1) introduced in [17]. We establish some weak and strong convergence results for satisfying condition (C) with the newly proposed framework uniformly convex real Banach spaces.

In a fuzzy metric space (X;M; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.    

In this paper, we introduce the notion of multivalued interpolative Kannan-type contractions. We also a more general version by relaxing degrees freedom powers arising in contractive condition. Gaba et al. (2021) recently pointed out significant error paper and Karapinar (2019), showing that particular type generalized contraction does not posses fixed point complete metric space. Thus, study m...