Müntz Type Theorems I

Some Fixed Point Theorems for Weakly Compatible Multivalued Mappings Satisfying Some General Contractive Conditions of Integral Type

Müntz Spaces and Remez Inequalities

Two relatively long-standing conjectures concerning Müntz polynomials are resolved. The central tool is a bounded Remez type inequality for non-dense Müntz spaces.

Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...

Generalizations of Müntz’s Theorem via a Remez-type Inequality for Müntz Spaces

The principal result of this paper is a Remez-type inequality for Müntz polynomials:

Remez-type Inequality for Non-dense Müntz Spaces with Explicit Bound

Let Λ := (λk) ∞ k=0 be a sequence of distinct nonnegative real numbers with λ0 := 0 and P∞ k=1 1/λk < ∞. Let % ∈ (0, 1) and ∈ (0, 1 − %) be fixed. An earlier work of the first two authors shows that