Abstract In the present paper concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and $( \alpha ,\beta ) $ ( α , β ) -cuts are introduced. Some common fixed point results for q-ROF presented in b-metric spaces using Suzuki-type contra...

R. Meyer and E. Mares [10] studied the logic CNR, a classical relevant logic with a modal connective. Such logic is of type S4. As it has been noted in [10], the addition of a modal operator in the language of classical relevant logic and the axioms φ ∧ ψ → (φ ∧ ψ) and (φ ∧ ψ) → ( φ ∧ ψ) do not necessarily produce theorems such that as (φ→ ψ) → φ → ψ or (♦φ→ ψ) → (φ→ ψ). These formulas are well...

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point the...

Let X be a second countable, path connected, compact metric space and let A be a unital separable simple exact Z-stable real rank zero C∗-algebra. We classify all the embeddings (up to approximate unitary equivalence) of C(X) into A. Specifically, we prove the following: Theorem: Let α ∈ KL(C(X), A)+,1 and let λ : T (A) → T (C(X)) be an affine continuous map such that (i) if h ∈ Aff(T (C(X))) i...

Sharp extensions of Pitt’s inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include HardyRellich inequalities. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and intrinsically are determined by their dilation character. In...

Let K[x, y] be the algebra of two-variable polynomials over a field K. A polynomial p = p(x, y) is called a test polynomial for automorphisms if, whenever φ(p) = p for a mapping φ of K[x, y], this φ must be an automorphism. Here we show that p ∈ C[x, y] is a test polynomial if and only if p does not belong to any proper retract of C[x, y]. This has the following corollary that may have applicat...

Let K[x, y] be the algebra of two-variable polynomials over a field K. A polynomial p = p(x, y) is called a test polynomial for automorphisms if, whenever φ(p) = p for a mapping φ of K[x, y], this φ must be an automorphism. Here we show that p ∈ C[x, y] is a test polynomial if and only if p does not belong to any proper retract of C[x, y]. This has the following corollary that may have applicat...

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work...

We define a rank function rk, mapping modal μ-formulae on ordinals below ω such that rk(μx.φ) > rk(φ(x)) for n ∈ N, with φ(x) ≡ x and φ(x) ≡ φ[x/φ(x)], and rk(φ) > rk(ψ) for all proper subformulae ψ of φ. The corresponding induction on formulae is thus justified by transfinite induction on ω. We then show that ω is the least such ordinal. Further, we give an algorithm to compute rk(φ) by primit...